How to evaluate a rational exponent 9^(3/4)

[@bprpmathbasics]

sqrt(20)-sqrt(5)=? (A) sqrt(15) (B) sqrt(10) (C) sqrt(5) (D) sqrt(2.5) Answer here: kzbin.info/www/bejne/ioDIkJaaebd3r6s

[@AGP335]

Am I the only one who worked it out in 5 seconds from the thumbnail?

[@kieranegan7335]

same

[@ryuk5493]

Same

[@anikchakraborty92]

ig it was pretty easy.

[@cameroncarpenter3480]

Same here

[@7mvg354]

Same it's like easiest problem for me 😂

[@ErtosAcc]

I'm really confused right now. This problem is really simple, so why is it considered hard? 9¾ = ⁴√9³ = ⁴√9² ⁴√9¹ = ⁴√3⁴ ⁴√3² = 3√3

[@meetshah4432]

That's what I'm wondering. This question is something that we solved in 8th/9th grade. How come this question even appears on a SAT paper?

[@jiviteshsharma8438]

@@meetshah4432the sat paper is very very easy. I recommend you to see the sample papers for the same.

[@lukeskywalker691]

Yeah so damn easy

[@rufatbabayev]

@@lukeskywalker691 and reading so damn hard

[@Vikram.201]

To gain views bruh.

[@jellyqwerty4391]

Notice that 9^3/4 > 9^1/2 Problem solved because then you can eliminate answer A, B, C

[@themathsgeek8528]

Nice!

[@darthmaul197]

10/10 solution

[@hanan2947]

Genius

[@chikezienestor3394]

Very Smart approach.

[@ankitlai]

Easy question made easier

[@kienthanhle6230]

9 ^ 3/4 is greater than 9 ^1/2, which is three. Therefore we eliminate A, B, C

[@snouthlly1479]

Wow good job! You just stole a comment!

[@kienthanhle6230]

@@snouthlly1479 nah I didn't. This is like such an easy elimination trick dude. If both you and me know how to walk, and you are older than me, doesn't mean I copied your movement.

[@Nico-Robin_07]

@@kienthanhle6230 you are correct so many people's in comments section say *you copied their comment* *copy bot* like these

[@magicofmaths5912]

Good job

[@seiseiruten-418]

@@snouthlly1479 he didn't, the comment stealer is actually you bro

[@devaorios5793]

These SAT Bois have it so easy man..

[@mu9190]

Ong

[@rufatbabayev]

I would love to see your face if you saw reading part

[@devaorios5793]

@@rufatbabayev Wasn't even prepping for the SAT's and I got a 1550 🤣

[@firezombie2731]

@@devaorios5793 If humbleness was part of the SAT, you’d get an 805

[@prodiptadas3305]

@@firezombie2731 you call it arrogance, but it's confidence. Sat is really ez, come to India my friend 😀

[@tahabukhari3189]

You used this method. Pft, this is how you do it the real maths way. First write (9)^3/4 as (4+5)^3/4. Now let x=4 and y=5. Therefore, we now have (x+y)^3/4. Let's factor out the x. [x^3/4 × (1+y/x)^3/4)]. Now we can use the Mclaurin expansion for the binomial theorem formula to get the following infinite expansion: x^3/4(1 + 3/4*y/x + (3/4*-1/4*(y/x)^2)2! ...) Now substitute in the values for x and y. 4^3/4(1 + 3/4*(5/4) + (3/4*-1/4*(5/4)^2)/2! ...) And boom we get. 3√3. How we got to the answer after the expansion is left as an excersice for the reader. Btw. For those people who couldn't see it. It was a joke.

[@tehnoobleader7673]

This is an easier method: We know √9(root to the power of 4 but I can't write it) is √3(square root) And 9^4/4 is 9 So if 1/4th power is √3, 9^3/4 is 3x √3 = 3√3

[@aksunonair]

HAHAHA

[@jeromenotfound_440]

Lmaoo

[@arkabanerjee1091]

@@tehnoobleader7673 r/whoosh/

[@dari9345]

@@tehnoobleader7673 You got it wrong at the end. Yeah, the answer is correct, the last step tho, isn’t. Just because 1/4th power of 9 is root3, doesn’t mean 3/4th power of 9 is 3 times root3, because by that logic, 2/4th power of 9 should be 2 times root3, or even more, 4/4th power of 9 should be 4 times root3, so it ain’t correct. Just do it like 1/4th power of 9 is root3, then you have 3^(3/2), so you can do root(3^3), which is root(9 * 3), take the root of both 9 and 3, and there you go, 3root3.

[@funangeld1556]

To solve this problem, I used the adding exponents with the same base rule to turn 9^3/4 into 9^1/2 times 9^1/4 and this gives me the answer directly since the first number is just the square root of 9, which is 3, and the second value is the fourth root of 9, which is the square root of 3 - thus 3 radical 3.

[@zainabhusain4076]

I liked how simple he made this question and made this easy to understand

[@ZootBurger]

I love how he's just casually holding a Pokéball 😀 Explains maths really well, too!

[@anildeshkar906]

Plus switches easily between red and black pens too. Very interesting

[@skyjoe55]

I could be wrong but i think his microphone is hidden in it

[@infienite9215]

@@skyjoe55 maybe a pikachu?

[@infienite9215]

@@skyjoe55 or perhaps that is his big math brain 🤯

[@paull2937]

9^(3/4) is like taking the 4th root of 9^3 or taking the 4th root of 9 then cubing the result. The cube root of 9 is 9^(1/3) which cancels. The 4th root of 9 is 9^(1/4) which also cancels. Taking the sqrt of 3 is like 3^(1/2) which can be converted to 9^(1/4) which also cancels. Thus, D is the only possible solution.

[@jaswik2023]

I did not understand ths can you elaborate pls

[@佐藤広-c4p]

Personally, I prefer to make the numbers as simple as possible, especially the exponential part in a fractional state. That is, 9^(3/4)=(3^2)^(3/4)=3^(6/4)=3^(3/2)=3^(1+1/2)=(3^1)*{3^(1/2)}}=3√3

[@nikhilsinghal5013]

exactly , isn't it to simple to be called hard

[@TURBO-gp5me]

You got 3^(3/2),if we do this like b^(m/n)=(n√b)^m=n√(b^m) as sair said th answer will be 2√(3^3)=3,then answer is wrong,is it?

[@佐藤広-c4p]

@@TURBO-gp5me 様(sama) Unfortunately, you are confused between multiplication and exponential calculation. 3^3≠3*3=9=3^2, 3^3=3*3*3=27, so √(3^3)=√27=√(3*3*3)=3√3, and √(3^2)=√(3*3)=√9=3

[@Professor_Sargeant_JAMS]

Once you have 3^(3/2), one thing I like to do is write 3/2 as 1 + 1/2. Then using b^(m+n)=b^m * b^n, this gives us 3*3^(1/2), ie 3*sqrt (3). I wish I could get these multiple options across to my students, to compare and contrast.

[@joeanil]

I love the way he holds the markets! :).... Great vids BTW.

[@reminderIknows]

also, 9^0.25 = 3^0.5, so B is C and since B is wrong, C is therefore also wrong

[@nathanielcabansay4535]

I initially used the fact that 9^3 = 3^6 = 27^2 so the term becomes 27^(2/4) 27^(1/2), then square root of 27 is 3 times square root of 3, which is D.

[@techno2371]

I computed it as sqrt(9^(3/2)), which is sqrt(3^3) or sqrt(27) which when simplified is 3sqrt3

[@yaseenelhosseiny]

At the end, you could get that 3^(3/2)=sqrt(27) which can be simplified to 3 times the square root of 3

[@alberthopfer3087]

To estimate an answer is a good way to start. With a fractional power like 3/4 ... know that the 3 will make the result larger and the 4 will make the result smaller. Always know that 1/2 is a square root.

[@arnavrevankar444]

I literally did this test today. It was in Practice Test 5, no calculator. I got the right answer, but did it the dumb way. Cubed 9 to get 729, then did the square root by hand (happened to know how) to get 27, and finally got to 3*sqrt(3). I'm laughing at myself now 😂

[@flameb0w402]

I realized you can do it this way: 9^(3/4) means that that’s 3 4 roots. A root of 4 is just the square root of the square root The square root of 9 is 3, and the square root of 3 is sqrt.3 That to the power of 3 is 3(sqrt3) Making it the correct answer

[@my.lionart]

That was my way, too! :)

[@kobethebeefinmathworld953]

The secret of Harry Potter (oops, I mean Dumbledore)

[@Gunman_boxing]

Platform 9 and 3/4 🤣

[@qwedcxzasd5317]

alreadey discovered

[@vijitjain17]

Bro such a hard question 😂

[@johnporcella2375]

Great use of "Notes" to state the general rule! Wish you had done that in your video where you suddenly brought in logs with no explanation/reminder as to how they work!

[@rssl5500]

Fourth root of 9^3 = fourth root of 3^6 =3 x fourth root of 3^2 = 3x sqrt3 Option D is correct

[@garrettdyches8426]

I knew it wasn’t B or A for the same reason, and to get rid of C, I realized that the 4th root of 9 is the same as the square root of 3.

[@AzureKyle]

Another way of looking at any number cubed, ie x^3, is that number multiplied to itself three times. So with x^3, that would be x*x*x. So, in this case of x=sqrt(3), it would be sqrt(3)*sqrt(3)*sqrt(3). sqrt(3)*sqrt(3) is the same as (sqrt(3))^2, which equals 3, so it becomes 3*sqrt(3).

[@jameshouse3329]

We can rewrite 9^{3/4} as (9^{1/4})^3, where ^{1/4} power is the same as taking the square root both times, so we can say that it is equal to sqrt(3^3) 3^3 = 27 sqrt(27) can be simplified because 9 * 3 = 27 and 9 is a perfect square 3 * sqrt(3) is the answer

[@GoodBoy-nx3oy]

Best way in my opinion: 9 can be written as √3^4 (√3^4)^3/4 will give √3^3= 3√3 I hope it helps🙂

[@forkey1595]

your video is underated. Love it, and I just subscribed :)

[@GodbornNoven]

3 sqrt3 kinda long eliminate the first two answers since it's obvious they're not correct due to the thing he mentioned concerning what roots represent. anyway, the third one is also wrong because of a simple reason 9^(3÷4)> 9^(2÷4) 2/4= 1/2 so the answer can't be smaller than the square root of 9,which is 3 sqrt 3 smaller than 3 so it can't be the Answer so it's D

[@TheBatugan77]

That instructor has big balls.

[@omaanshkaushal3522]

I did it by splitting it as 9^1-1/4... Simplifies to 9/4th root of 9 or 9/sqrt3 which is ofcourse 3sqrt3

[@aarav7851]

That's too easy Use calculus somehow Anyways I did the same as you

[@omaanshkaushal3522]

@@aarav7851 I am a 10th grade student and thus don't know much about Calculus

[@aarav7851]

@@omaanshkaushal3522 so you're the same as me

[@omaanshkaushal3522]

@@aarav7851 Yes bro

[@StevenTorrey]

While it may look obvious, laying out the steps logically, show why (D) is the right answer.

[@spikyowo7519]

to be fair just do it the reverse way from roots to exponential, seems quicker

[@domc3743]

Process of elimination works too

[@jjtucker]

My soln: fourth root(9^3) = fourth root(3^2*3^4)= 3*fourth root(3^2) = 3sqrt(3)

[@maverick5056]

When you realise that you learnt this same problem in class 9 and it gets asked in one of the hardest exam....

[@homersimpson8575]

Sat is more like the easiest test.. Look up Gaokao or JEE if you think SAT is hard

[@rohitsankhala6273]

SAT is hard? Nice one 😂🤣

[@adityachaku5402]

This is such an easy problem....

[@JamesJoyce12]

never ignore the brute force method - quick and dirty - prefect for future engineers - 9^3 = 729 [do it in ur head] then square root of that is 27 [ ur head again] and the square root of that is a bit over 5 - hence answer "d" is a "bit" over 5

[@bx7257]

The level of unsatisfaction is pretty damn high but well it is not stupid if it works

[@rickguerrero2282]

Nice work!!!

[@MGEditz007]

Hi, 9^(3/4) = 3^2•3/4 = 3^(3/2) Now divide it into easy form, 3•3^(1/2) = 3√3

[@MGEditz007]

Btw, why is this a hardest SAT rational number problem ?

[@vortexlegend101]

There’s a much easier way to do it without knowing many power rules. 9^0.5 =3 9^1=9 Option D is the only option between those values

[@ameykadam5195]

That's not a method that's just being lucky with options

[@nol2521]

@@ameykadam5195 take advantage of multiple choice, while it may spoil you it’s definitely convenient

[@nupursharma6869]

@@nol2521 definately convenient but not something you can rely on

[@nol2521]

@@nupursharma6869 that’s true, I don’t mean to say you should rely on it but when you have time pressure or you can’t directly answer a question, it’s useful to know the little tricks just to increase your chances

[@CollDott]

I didn't go through all that process of dissection. I looked at all four answers and figured D has a more likely chance than the other 3 ! 😆 So that it!! The other 3 appear to have been manipulated in a way to fool around that kind of thing!! So please love me!!

[@aradhyasingh4043]

Best way is write 9^3/4 as 3 as the base so 3^3/2. The we can write it as 3^1 × 3^1/2 thus 3^1/2 is nothing but root 3. So Ans. 3√3.

[@Gunman_boxing]

The small 2 is squared and the small 3 is cubed

[@SlayerEndX13]

9 = 3^2 3 = sqrt3^2 Thus, 9=sqrt3^4 sqrt3^(4*3/4) becomes sqrt3^3 That's sqrt3*sqrt3*sqrt3, which equals 3sqrt3; the answer is D.

[@gauravchauhan554]

Idk why this is a HARD SAT problem...it legit took me 7-8 secs to do it mentally.

[@absidyabsidy2727]

wow you must be so smart!

[@gauravchauhan554]

@@absidyabsidy2727 no brother…..i am not flexing or trying to put anyone down but literally all of my classmates can do it and it’s my last year of high school. We Indians do prepare for an engineering exam and if this type of questions come in that. Government will probably take actions against the organisation that conduct this exam……why are the questions so easy….

[@absidyabsidy2727]

@@gauravchauhan554 learn about the American university admissions system before talking shit. There’s a reason the top American universities crush the IITs. The SAT is not an engineering university entrance exam, it is a general exam for everyone who wants to enter university, arts and music and everything.

[@gauravchauhan554]

@@absidyabsidy2727 i legit said not trying to put anyone down…..what u expect?

[@absidyabsidy2727]

@@gauravchauhan554 it’s because nobody cares that you can answer this question in 5 seconds or whatever. That doesn’t make you smart or interesting. I don’t understand why Indian students feel the need to bombard every video and talk about how easy the question is and how quickly they can solve it.

[@gabrielbergens4806]

How i did was write it as 4sqrt9^3 = 4sqrt81 * 4sqrt9 = 3*4sqrt9 = 3*sqrt3

[@dselvy]

Good review 👍

[@yumikiss13]

I am happy that I still know how to find the correct answer after 20 years from school.

[@striker1711]

i had this concept in my 9th grades

[@thehindu912]

Me in 8th

[@nirupam5759]

I just did 9^3/4 = 9^1/4 * 9^1/4 * 9^1/4 Now we can write the 9 as 3^2, this it becomes 3^2/4 which is equal to 3^1/2 so the answer becomes 3√3

[@ritankarmondal8907]

Ans-d 3root3

[@cdmcfall]

Given the choices, I guess technically you could do it by expanding it to factors of 3, then simplifying, but this is the equivalent of adding on one's fingers: 9^(3/4) = √(√(9^3)) = √(√(3 × 3 × 3 × 3 × 3 × 3)) = √(√3 × √3 × √3 × √3 × √3 × √3) = √3 × √3 × √3 = 3√3

[@spooky2526]

9^(3/4) = ((9^1/2)^1/2)^3 = (3^1/2)^3 = sqrt(3) x sqrt(3) x sqrt(3) or 3sqrt(3) I hope this isnt actually a hard sat problem, I would expect any competent math student to be able to do this in their head in about 20 seconds at most

[@destroyerthunder678]

I think less than 20 seconds.I am 15 years old and if this is a hard problem I can get a good score in sat

[@vladosholodos.]

Мужик то реально старается, молодец!

[@OnlyAllah-pr4uo]

Simple question 9power3=729 Double under root of 729=answer

[@andrewliang5818]

9^3/4 =(((9^(1/2))^(3))^(1/2)) = (3^3)^(1/2) = sqrt(27) = 3sqrt(3) Not sure about the method, but thats what I came up with

[@SyedAhmed-lv3kh]

thanks i wanted to know how to solve this properly

[@Han-ys8pp]

Was my primary school the only school that didn't have questions like these for their SATs papers??

[@elweewutroone]

UK SATs (pronounced ‘sats’) are not the same as US SATS (pronounced ‘es ay tees’). The UK SATs are for primary school (10 to 11-year-olds) pupils (nomenclature: in the UK, students are at or above secondary school level while pupils are below) for better tailoring in secondary schools, while the US SATS are national exams for high school students (all young learners in schools are students in the US) to get into university/college, and are therefore at a much higher level.

[@Han-ys8pp]

@@elweewutroone Thank you for explaining that to me 🙂

[@xSayf_Rx]

Who is watching this whilst fasting in ramadan just because they are hungry 😂

[@elsenored562]

Sqrt(3³)

[@ramlaaal]

math is really beautiful.

[@randomname9291]

The way I solved it was the following 9^(3/4)= fourthroot(9^3)=fourthroot(729)=fourthroot(27^2)=sqrt(27)=sqrt(9*3)=3sqrt(3)

[@zippymax1]

I was never good at such arithmetic. I just got my Physics degree and made my computer spit out the actual numbers lol.

[@YourGirl2628]

This is what i am learning in 9 grade

[@r0cketplumber]

9^.25 is root3, cube that to get 3 root3, D.

[@robme9845]

Since 9 raised to the power of 3/4 is greater than 9 raised to the power of .5 which is the square root of nine which is three the test taker only needs to select the answer which is greater than 3 which is D rather than wasting 10 minutes on complicated root calculations.

[@switchydoe]

u didn't have to do all of that mate, just split the exponents and do the easy powers

[@jamescollier3]

he's teaching

[@dushyanthabandarapalipana5492]

Thanks!

[@ichvvhovxugcvuhi3522]

Was quite that you even went through simple question like this. Your others videos are a lot tougher than this. Capturing another segment of audiences now :p ?

[@scareflare7553]

If your eyes didn't go to the "HARD SAT" highlight, then......fine Plus, there are other users who may sometimes confuse, while most of us did it easily...

[@gullivert3076]

Merci pour votre leçon

[@jackphillips3354]

Okay, before I continue, I put D to put my College Algebra studying to the test. I was answering a whole other question: last night, I think it was sqrt 20-sqrt 5. This branched off into 2*sqrt 5-sqrt 5=sqrt 5. To answer THIS question, I say it’s B, based on the denominator of the fractional exponential value. If I’m wrong, please let me know, and provide me with a step-by-step explanation. I intend to make a living off of this subject.

[@jackphillips3354]

Okay crap! The answer to this one is D: 3*sqrt 3. I think I can see why though. 9 is 3 squared for starters. So that crosses off squared, and reduces the denominator of the fractional exponential power from 4 to 2. Which in turn produces three sqrt 3s. So multiply the first two, and the answer is 3*sqrt 3. It’s okay, I got it!😅⚾️🔩🧠🌎

[@CD_3074]

we do know 9^1/4 tho because it's just (9^1/2)^1/2 which is 3^1/2, then just cube that √3 and you get 3√3

[@mtc-j9i]

9^3= 729, which is the same as 3*3^4…. So if you do the fourth root of 3*3^4, you get 3root3.

[@youreyes46]

This is GOOD 👍

[@ZombieHoards]

Everyone solving the question in the comment box. Me: its the platform 9¾, way to HogWarts.

[@cdmcfall]

Crap, I messed up my calculations at the very end, but I was on the right track. Here is what I did: 9^(3/4) = (9^3)^(1/4) = ((9^3)^(1/2))^(1/2) = √((9^3)^(1/2)) = √(√(9^3) = √(3√3) In hindsight, I realize that last line should have been √(9√9) instead of √(3√3), which would have obviously led to: √9 ⋅ √(√9) = 3 ⋅ √3 ≈ 5.196

[@nekogod]

I guessed in a slightly different I knew that anything raised to the power 1/2 is the same as a square root and sqrt of 9 is 3 so 9^3/4 would be bigger than 3

[@juthtime]

You are just making more complex. 9^3/4 can be changed into 9^(1/4).9^(2/4). it means (3^2)^(1/4).(3^2)^(2/4). By this way you will get 3√3 faster

[@matthewbecotte9839]

Em thích và ngưỡng mộ thầy lắm. Thích vì thầy vui vẻ hòa đồng dễ thương nói chuyện thật thà và chia sẻ những gì thầy biết đến cho mọi người . Còn ngưỡng mộ vì thầy có 1 cô vợ hiền lành đẹp gái nói chuyện nết na thùy mị. Và may mắn thầy có được gia đình vợ yêu thương giúp đỡ ❤❤❤

[@amnapatsawan]

This is how I solve 9^3/4 = 3^ 2(3/4) = 3^ 3/2 = √3^3 = √27 = 3√3 is it correct? Sorry for my bad english😂

[@Shortypie]

That's how he did this.

[@amnapatsawan]

@@Shortypie Oh my bad

[@shreyoshreemahato]

The answer is 3√3 solved in less than a min

[@absidyabsidy2727]

wow you must be so smart!

[@DRAAi_wHity]

Goated teacher

[@codewithraiju1424]

Such an easy problem..

[@arnavsrivastava458]

This question so easy that i guessed d looking at the preview of video. Lol

[@deverathkumar8994]

Let me present my way 9^3/4=9^(1-1/4) =9/(9^1/4) =9/3^(1/2) 3×3^1/2 D correct option Very easy

[@robertwalker2052]

You answered it because you are holding a Magic 8-Ball.

[@mistadude]

It took me more than half of the video to realize he was holding a pokeball

[@faizkureshi8925]

Why there's the pokeball in hand???

[@ipostbecauseimbored]

I don't get the last part when you said "and now this thing (points at Square root of 3)² is just this (cancel ²) and that (cancel Square root) and 3 like why you cancel them and why you leave 3? 4:45

[@ruilongsheng2845]

3sqrt 2 * 9 sqrt 2 = 3√3

[@theliberandu3007]

I could do that in my mind.

[@greatkiddo7194]

4:55 why was the denominator of the exponent (3/2) ignored?? I dont understand

[@joanmorris4052]

😱 OMG 😳 amazing U make me understand √ I struggle with it but now I start 💕 it ** U make it so easy to learn Please 🥫 u teach us trigonometry

[@mohammadrezasaeidi8230]

answer is =3

[@niceguy999918]

I don't get it. How did it become a 3 and where that 2 come from. You can cross multiple the the exponent numbers. How? How do you know when to cross multiple?

[@gogomaths]

I had seen the preview and thought that there was "q", not 9😂. I could't compete this task, lol

[@kalyanbasak6494]

🙏🏻 proffessor sir answer sharing 3 3/²,no option