08 - Rules to Multiply & Divide Radicals in Algebra (Simplifying Radical Expressions)

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In this lesson, you will learn the rules that are needed to multiply and divide radical expressions in algebra. This is made much easier now that we have covered that fact that all radicals are really fractional exponents.
Because of this, all of the rules to multiply and divide radicals are really the same rules that we use to multiply and divide exponents.

[@LCC2731]

This guy is underrated. These rules are super important as you move to calculus and most people don't understand them. Thanks for the vid

[@user-qy6tu9ip9v]

Hey buddy. Could you possibly write down a list of skills that I should know from pre-calculus so I can do well in calculus. I don't mean to bother you.

[@LCC2731]

@@user-qy6tu9ip9v Everyone's experience will be different; therefore, take these suggestions with an open mind. Three main things I wish someone had told me before taking Calculus 1 would be; first know the Unit Circle values exceptionally well. Memorizing the unit circle values will make your calculus experience considerably easier and save you time on homework and exams. The second tip I would offer, which is often overlooked, would be to strengthen your algebra skills as much as possible, especially simplifying rational expressions, rationalizing the numerator/ denominator, and exponent rules. Overall, having a solid foundation in algebra will make Average Rate of Change, limits, and chain rule problems, just to name a few, much easier. Lastly, knowing the graphs and aspects of common functions such as f(x)=squarootx, f(x)=x^3, f(x)=ln(x), f(x)= e^x, and any other common functions will make your life easier in Calc 1, because you will work with these graphs quite often throughout the course. Especially when you start working with extreme values, concavity, and inflection points.

[@joeanderson2024]

@@user-qy6tu9ip9v working off @Lamond first point, you will have to know the radian measurement for the main angles for trig (0*,30*,45*,60*,90*). I’m using * as a degree symbol since there isn’t a degree symbol on a keyboard They are sin0*=0, sin30*=1/2, sin45*=√(2)/2, sin60*=√(3)/2, and sin90*=1 Cos of angles (0*,30*,45*,60*,90*) is the same as sin (90*,60*,45*,30*,0*) respectively I could never remember the table because the numbers (1/2 and √(3)/2, for example) don’t make sense because they don’t really have a pattern, some have square roots, som don’t. That’s the biggest reason I failed trig. I later learned all of them have square roots, Sin (0*,30*,45*,60*,90*)=√(0)/2=0/2=0,√(1)/2=1/2,√(2)/2,√(3)/2,√(4)/2=2/2=1 respectively Cos(90*,60*,45*,30*,0*)=√(4)/2=2/2=1,√(3)/2,√(2)/2,√(1)/2=1/2,√(0)/2=0/2=0 respectively Seems very easy when somebody tells you but not something you would think about on you own.

[@user-qy6tu9ip9v]

@@joeanderson2024 So all I really need to know is the first quadrant.

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[@squ3g]

I have a question. If 2^3 x 2^3 = 2^6 then why would a fractional exponent not be added? like for example @10:27 2^1/3 x 2^1/3 should = 2^2/3, no? I mean multiplying exponents we add... and 1/3 + 1/3 = 2/3, no?

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Glad you liked it

[@richardhallahfarkollie4345]

Thank you for making me to understand readical,

[@Juan-yj2nn]

Hey. I think a good way of explaining the very first rule would be to say: Well, you know, saying that √ab = √a * √b is literally saying that this number (√a * √b), when squared, gives you ab, right? So if you square it, you have (√a * √b)²= (√a)² * (√b)² = a * b = ab. And there you go :) Of course, this only works if both, a and b, are positives or equal to zero. Be careful! PD: The square root, denoted as √, means "POSITIVE square root". So you also have to have that √a * √b is a POSITIVE such that when squared it gives you ab, as we have shown.

[@joeanderson2024]

How do you get the exponent up like that. I al do 2^2 as 2 squared. It gets very confusing if you have an exponent such as (2/8)+3

[@tacosyogan9914]

Super Teacher in action!

[@StoryTeller796]

Before I watch this video, here's my theory as to how radicals work. They basically have the same relationship with division that powers have with multiplication, with some extra rules because reducing and multiplying something is much harder than simply adding or subtracting it (the number 0's multiple paradox's or complications can attest to the court of that along with negatives). Yeah, that makes sense when you put it that way, fractional exponents. What negatives are to positives and fractions to multiplication. Now time to simplify the concept and break it down.

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[@newtao8384]

Hi from Brazil! What can i do to symplify/solve when i have something like √(2- ∛5)?

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The answer is in decimal.

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[@itzzkundan]

I have a question in mind. Why the laws of exponents do not work properly for the base belongs to negative real numbers. For example: (-2)^(12÷4) = (-2)^(3) = -8 we know that. But what if do it by laws of exponents, (-2)^(12÷4) = ((-2)^(12))^(1÷4) = (4096)^(1÷4) = 8

[@itzzkundan]

Another question, my scientific calculator showing that , 3√(-8) = -2 And also it is showing (-8)^(1÷3) = 2 × 3√(-1) = final in expanded form it is complex number. Really confused for these negative bases. And I know about exponential functions also in detail. Base cannot be negative etc. So don't give that damn answer. Just give me logical answer if possible. Or make a video on it if possible. Thank you.. Kundan from India 🙏

[@mathfullyexplained]

Even exponents of Negative numbers are positive. Your example does not work. Exponent rules apply to positive bases. Try my channel mathfullyexplained

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Make a video about properties of radicals

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good job, and thankyou. I find radicals are brain bending

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21:00

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1:49

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people in what country write radical sign that way?

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Just use the numbers please. For my very confused mind cannot make a number out of a letter...sigh.

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If this also applies to subtraction, you can find proof that i = -1

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him: ok lets add 1 more here because I like even numbers *jots down a 5*

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