How do you take the Square Root of Fractions? Let’s see…

How to take the square root of fractions.
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[@lovernotfighter]

I did this in college and I can follow you easy enough. My problem is doing it without your instruction. Very difficult. Thank You Sir for your excellent instruction.

[@robertakerman3570]

that was fun/refreshing

[@ootlattle5450]

Curses, FOILed again…..

[@gum9871]

Thank you so much for making this video, Algebra KZbin teacher. I gained clear understanding of how to solve problems involving square root of fractions. I wish you well, continue making videos you're passionate about. ❤❤🙏🙏

[@pseuda]

11:20 - the whole class is good, but this last problem starting here is really good!

[@johnnyragadoo2414]

Fun stuff! I found algebra and trig incomprehensible in school. Now I can close my eyes, let circles, triangles, and squares float around, and visualize all kinds of things of interest. I probably don't get out enough lately. Blame the recent pandemic... One question, though. Rationalizing either the numerator or the denominator is easy enough but either way you still have an irrational value. Why is a rational in the denominator of greater usefulness than a rational in the numerator? If the value is irrational, you can't have both and if you end up needing the reciprocal you end up with an irrational in the denominator once again. Also, fun visualization - consider a rectangle of sides 16 and 36 (two perfect squares). The area will be 576, or 24 squared. Now think of a square with sides of 24 (area 576). But don't think of the sides being measured in units of one. Measure the sides in units of the square root of 36, the long side of the original rectangle. The sides are each four units-of-6 because four is the square root of the short side of the rectangle. Sides that are four units-of-6 are 24 units in length. 24 squared is 576. The sides of the square are the product of the square roots of any factors that give you the original area. In other words, the side of a square of equal area to a rectangle is the geometric mean of the sides of the rectangle. 4 squared divided by 6 squared equals (4/6) squared. Thanks, man - I learned much!

[@argonwheatbelly637]

It's easier to add and subtract fractions if the denominator is rationalized. It's not required. It's merely a convention.

[@johnnyragadoo2414]

@@argonwheatbelly637 Aha! I knew there was a reason. Thank you!

[@marytredinnick3366]

Thank you for helping me understand the conjugate!

[@tomasnicholas1881]

.....great work....thanks.

[@thomasharding1838]

Thank you for the video!

[@zeromotivation1817]

would you further simplify the denominator to 4( 1-2(sqrt2))?

[@thenelcomics1997]

So wonderful work... Following you from south Sudan 🇸🇸

[@yolandarios8468]

Thanks. I love the way you teach. God bless you

[@stumbling]

In the last one we can also remove the minus from the denominator: (8√2 - 4)/7

[@kevin_g1164]

If you use the other solution (non-principle) for the SQRT of 64 being -8 you end up with +9 on the bottom line. Is that also acceptable?

[@w2jdb635]

Wish I had you as a math teacher in 9th grade algebra.

[@ianmurphy2804]

Very well explained.

[@nuhumaishanu6944]

Can't we multiply both numerator and denominator by -1 to get rid of the negative sign in -7

[@edwardhuster8466]

These help fight dementia.

[@Kobe_Abogutal]

2:30 the solving starts here

[@josuepadilla516]

Thanks 🙏🙏.

[@elc3can]

Thank you.

[@Meggyweggy_961]

what happened to the multiplication sign that was in between the original equation and the conjugate on the numerator before doing FOIL? I only see the (-) sign that wasnt there

[@shakur2592]

thats part of apply conjugate

[@mikesullivan5219]

Thanks, I learn'ed ta remove da irrational behavior in da denominator, an a use a conjugate ta multiply da numerator!

[@ds61821]

What about getting rid of the negative in the denominator? Multiply both sides by -1/-1?

[@merrylbutcher4965]

Which two sides? Each is an expression which has to be simplified. -1/-1 is equal to 1, so you can multiply anything by this without changing it's value.

[@johndemartin1786]

A fraction with a negative sign anywhere ("top" "bottom" or to the side) is a negative fraction. So: -a/b = a/-b = a/b with the sign to the left of the entire fraction. Your choice. Most teachers I've come across don't like the negative in the denom. But it's not "unacceptable" like having a sqrt3 in the denom. I prefer the negative with the numerator. Tohmaytoh, Tohmahtoh

[@vanciejohnson176]

Your are a genius

[@zonked1200]

Shouldn't you factor out the (-1/-1) part of the third answer so that it ends up being (-4+8*sqroot(2))/7?

[@amitabhjayaswal]

Good topic to learn. Thanks that you explained it. Which software or platform are you writing on though? I never came across any such multi-color, multi-functional online class board. Please do answer. Thanks.

[@robertakerman3570]

people have asked B/4

[@alrees61]

Paint App

[@amitabhjayaswal]

Thanks.

[@herkermit9872]

Never heard of FOIL or I was looking at a girl two rows over. FOIL is good. She cut her hair 😢

[@edwardhuster8466]

Because 3 phase electrical generators use square root 3. Which is approx 1.732. Lot electronics math used in electrical and it's 1st cousin electronics. Thx Tesla.

[@amitabhjayaswal]

Share the link of the FOIL video lesson as well, please.

[@argonwheatbelly637]

Of you learn to multiply polynomials, the order in which you would naturally multiply binomials just hairbrush to be FOIL. It's a nifty mnemonic, but learn the full way. After all, what about (x+3)(x²+3x+5)?

[@andrewm6424]

BUT you COULD do one more step on the last question. To fully simplify it you COULD say negative (4 - 8sqrt2)/7

[@pseuda]

This is a good point!

[@donaloloinsigh3847]

19:43 what a teacher who can’t follow on to a conclusions without trying to digress and telling how difficult the question is. D o l

[@DerekMitchell]

It’s actually better as 8.2*½ - 4 div by 7

[@pjv767b5]

Why do we still deal with fractions when we can use the metric or decimal system? Fractions are the most involved system to devise, add, subtract and multiply.

[@jolyonwelsh9834]

An irrational number is just a fancy term for a decimal or a non integral number.

[@williambullock641]

I would have written it( 8(Square root of 2) minus 4) over 7

[@David-yu9iz]

Kids....this never comes up in the real world. Nor does 2 trains on the same track. But....what time should you leave to pick up a child at soccer practice that ends at 7 and a child at 715 10 miles from the first when you work until 8?

[@williamturner1517]

It's not my "attention span". It's a question of "interest span".

[@michaelmcarthur8364]

In our world of practicality needed for everyday solutions, how does a fractional square root into such an equation equate into a solution to the building of a bridge, the construction of a skyscraper, the combustion of an engine? What is the reason for its purpose as a benefit to our survival as humans?

[@pseuda]

I can't assume your question is for real, but you are right, maybe solving fractional square root does not equate into the solutions you mentioned - as far I assume you perfectly know the calculation for every one you mentioned plus others as well - and, please, note this is basic maths... For pupils maybe this is useles for their survival as humans, but it is required for their survival as students, and note again that solving fractional square is needed for their everyday solutions.

[@argonwheatbelly637]

Why do we rationalize the denominator? Because it's easier to add and subtract fractions if the denominator is rationalized. It's not required. It's merely a convention.

[@Naomi.Galowa-qr7uv]

Home school learning

[@danieldennis9831]

First is 3/4 second is √3/3 third is ... I am not certain. I guess I watch the video now.

[@danieldennis9831]

Okay .. Forgot that method. Thanks.

[@tonywright560]

I don't understand why you have to rationalise the denominator. If the number is the same the number is the same. Why is form important?

[@ElixerJohn]

Because it's the mathematical law.

[@philliphaley1241]

I knew that you would get this wrong before you even started...YOU ASSUMED THAT EVERYONE KNEW THAT THE SQUARE ROOT OF 9 WAS 3 ETC.

[@adeliaaf5649]

If you’re doing fraction sqrt then you should know basic square roots

[@lokani8814]

Why do you have to change 1/√3? When doing calculations for physics problems you just want the answer or an estimate of the answer. √3 is about 1.7 and 1/1.7 is about .58. Depending on significant figures .58 should work fine for the answer. Why functionally do mathmaticians dislike irrational numbers in the denominator? It feels like unnecessary steps to finding the solution. Functionally it does not make a difference.

[@argonwheatbelly637]

It's easier to add and subtract fractions if the denominator is rationalized. It's not required. It's merely a convention.

[@lokani8814]

@@argonwheatbelly637 Thank you, that makes a lot of sense.

[@martinhutton6294]

I don't understand why it is acceptable to have an irrational numerator but unacceptable to have an irrational denominator. It seems like an arbitrary preference.

[@billythebootlegger.4376]

The easiest way to solve it is to start by calling it MATHS it's PLURAL.......

[@argonwheatbelly637]

No, it's both ways, depending on your location.

[@johnbannister9212]

You didn’t just labour this, you abominated it.