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### Course: Algebra (all content)>Unit 11

Lesson 6: Simplifying square roots

# Simplifying square roots (variables)

A worked example of simplifying radical with a variable in it. In this example, we simplify 3√(500x³). Created by Sal Khan and Monterey Institute for Technology and Education.

## Want to join the conversation?

• Hi all.
Looking for some help with the following:

3/√63

So far I have:

3/√63
3/(√9 x √7)
3/3√7
√7

The answer in the book I'm studying from, however says that the answer is:

√7/7

How does one arrive at this answer?
• Hi. When working with radicals, you can't have a radical for a denominator. This is not considered proper in Algebra. So your answer to
3 / √63 would eventually equal 1/ √7.
In order to make it algebraically proper, we have to multiply it by √7 / √7 (which is equal to one, so we know it won't change the value of our equation).
So we get:
`` 1 / √7 * √7 / √7 =√7 / √7 * √7√7 / 7``

We know that √ 7 * √7 is the same thing as √ 7*7, or √49, which is 7. That gives us the final answer of √7 / 7 which can't be reduced any farther.
Hope this helps.Sylvia.
• This is hard stuff and he seems to be blowing through it rapidly like it's just review. What is the previous video he keeps referring to in his commentary? The video I see before this one is entitled "Simplifying Square Roots" and he doesn't seem to cover a lot of this. Am I missing something?
• I'm with you. Last vid is the same for me, "Simplifying Square Roots". I watched and understood all of the previous vids leading up to this one and he did blow through this one without slowing down to take the time to really explain why he's doing that. Yet he'll go over extremely simple concepts ad nauseam
• You confused me...Why can't X be a negative number?
• coughs I'm late 8 years but whatever.
Simple: you can't have negative rads. Use a calculator but a negative number like -1, and it will say "Error" or something like that.
There are no two numbers that when you multiply them twice (like 2 • 2, aka 2^2), you cant get a negative number. Like a negative times, a negative is positive, and a positive times a positive is a positive.
And you cant multiply two different numbers (negative and positive) in a rad because rads represent a number multiplied by itself to get that number inside the rad.
• I don't understand most of this. I think i'm missing a video.
• I'm sorry, but can we try one WITHOUT an x? I'm going into Grade 11 and never learned this. How do you simplify something like (sq root)45?

In the practice, there are questions where c= sq. root 45 and they need a simplified radical. How do you do that?
• I'm gonna use sqrt as square root
sqrt(45) = sqrt(9*5) = sqrt(9) * sqrt(5) = 3 * sqrt(5)
Hope that makes sense! :)
• If you watch these videos in the order the lessons are published for Algebra basics > foundations > square roots module, there are a lot of references in "Simplifying square roots (variables)" to the previous video ( and ). But the previous video is about fractions, not variables. I had to jump over to another module (Math > Algebra 1 > Exponents & radicals > Simplifying square roots) to find the video I THINK he's referring to, "Simplifying square root expressions".

Can anyone at Khan Academy explain to me why this learning module would leave out lessons required for completing the content?
• what happens when the absolute value of a number turns out to be a negative, not a positive
• The absolute value of a number is always positive and is will never be a negative.
• Why does Sal keep saying "the principal root of..." as opposed to "the square root of..."? At I heard him say "the square root of, or the principal root of..." so does that mean they're the same thing? Because it appears as if he sort of corrected himself.
• could you not just do +- (the plus or minus sign -- my computer doesn't let me insert special charactors)?
• I'm at a loss, The quiz is asking questions that the videos have no explanation of. I have x^9, but the video only explains how to factor it one time..
• Matthew,

This video is part of the Algebra I course and is not meant to stand alone. Many of the concepts applied here are explained in previous videos in this course and in the Pre-Algebra course.

Take a look at the outline of Algebra I (https://www.khanacademy.org/math/algebra). You may want to go back to the previous videos in Rational exponents & radicals or to the Exponents, radicals, and scientific notation section of Pre-Algebra (https://www.khanacademy.org/math/pre-algebra)

The Law of Exponents tells us

x^a * x^b = x^(a+b)

Therefore

x^4 + x^5 = x^(4+5) = x^9

x^4 is a perfect square - x^2 * x^2

You could also consider

x^9 = x * x * x * x * x * x * x * x * x

x^9 = (x * x * x * x) * (x * x * x * x) * x

x^9 = x^4 * x^4 * x