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### Course: Class 8 > Unit 6

Lesson 1: Cubes and cube roots 6.1# Simplifying a cube root

Simplifying Radical Expressions1. Created by Sal Khan and Monterey Institute for Technology and Education.

## Want to join the conversation?

- how do you find all the real fourth roots of numbers?(12 votes)
- Square root it and do it again. Thats all(14 votes)

- Why did the cube root of -1 turn out to be -1 ????(7 votes)
- I see that people already answered to this question, but to make these kinds of things simpler, just look at the numbers. Even numbers(power) will always change negatives to positives, for example, -1 to the 100th power will equal 1. On the other hand, you might have as well guessed, odd numbers(power) will make the number stay as a negative, for example: -1 to the 99th power is -1. So even if they ask you a question with big powers, you can always see if the power is a even number or a odd number to determine if they number will be a negative or a positive number.(1 vote)

- None of the videos deal with fractions. How would I go about finding the square root of fractions? Can they not be simplified?(14 votes)
- I think you solve the fractions the same way the ones shown above are solved you just divide the common factors instead of multiplying them.(4 votes)

- Is there a video of0:37where he goes through the rules of how you know what something is divisible by?

It's another part of my swiss cheese math brain I need filled in.(8 votes)- What Sal is doing at0:37is called prime factorization. There is actually a topic entirely focused on prime factorization. You can find it here: https://www.khanacademy.org/math/arithmetic/factors-multiples/prime_factorization

There is also a topic focused on recognizing divisibility, which will help you to understand what a given number is divisible by. You can find that topic here: https://www.khanacademy.org/math/arithmetic/factors-multiples/divisibility_tests(3 votes)

- I'm trying to do the pythogrean theorem but in the answer block it asks for a simplified radical and i watched this video but it still does not make any sense...

any ideas?(5 votes)- A radical expression is an expression that includes the root of a number. Am I right in guessing that the answer space for the pythagorean theorem problems includes a regular box and a box under a square root sign? If so, then you simply need to simplify the square root of the answer.

For instance, if you had a right triangle with legs 2 and 4 and hypotenuse c, then you use the pythagorean theorem, which is a^2 + b^2 = c^2.

Add the squares of the legs (a and b in the equation above) to get 2^2 + 4^2 = 4 + 16 = 20.

To get c, you take the square root of a^2 + b^2, so c is equal to sqrt 20.

Because 4 times 5 = 20, you can get sqrt 20 = sqrt (4 x 5)

This simplifies into (sqrt 4) x (sqrt 5) = 2 x (sqrt 5), which would be the answer.

Hope that this helps!(5 votes)

- In the Simplifying Radicals video, u simplyfied the radical by using the following formula:

Problem: simplify the square root of 72

Step 1) the square root of 72 = the square root of 36x2

2) the square root of 36x2 = 36 squared x 2 squared

3) the square root of 36 = 6

Answer: 6 x the square root of 2

In this video u simplified radicals by using a factor tree. Which formula should I use???(6 votes)- you can use the factor tree or any prime factorization method that you find useful because they all work. using the factor tree is helpful at first because it lais out all the primes and is easy to count when grouping together the primes.(3 votes)

- so a square root is like dividing the number by 2(1 vote)
- No, though there is a connection with square roots and the number 2. Multiplying 2 of the same number (8*8, 2*2, 5*5) results in a square number.

A square root is working backwards. Finding a square root is the same as asking, "What number, when multiplied by itself, equals the number I'm trying to find the square root of?"

I hope that helped.(10 votes)

- how would you solve if you had a radical with a number then multiple variables in it(4 votes)
- at1:46y does he keep adding 7 onto the end ?(3 votes)
- He is not adding 7. He is multiplying by 7. That is because the prime factorization is -1*7*7*7.(1 vote)

- wait, @0:18where did the exponent 1/3 come from? what does that mean?(2 votes)
- like if we are told to find the square root of a number , we can write than number inside the radical sign or we can write number raised to the power 1/2 , so similarly if we are told to find the cube root , it can also be written as the number raised to the power 1/3 instead of placing that radical sign :) I hope this helped you !!(2 votes)

## Video transcript

We're are asked to find the
cube root of negative 343. Or another way to think
about it is some number that when I multiply it
by itself three times, I'm going to get negative 343. Or another way to view
it-- this is the same thing as negative 343
to the 1/3 power. And the best way to
do this is to really just try to factor this out. So the first thing
that we could do-- so let me just factor negative 343. So the first thing
I'd like to do is just factor out
the negative 1. So this is the same thing
as negative 1 times 343. And let's think about this. Is this divisible by 2? No. Is it divisible by 3? Let's see-- the digits do not
add up to a multiple of 3. They add up to 10. So it's not divisible by 3. Not divisible by
4 since it's odd. Not divisible by 5 because it
doesn't end with a 5 or a 0. It's not divisible by 6, because
it's not divisible by 2 or 3. Is it divisible by 7? Let's check this out. So 7 goes into 343-- 7
goes into 34 four times. 4 times 7 is 28. 34 minus 28 is going to be 6. Bring down the 3. 7 goes into 63
exactly nine times. So then we end up-- so 9
times 7 is 63, no remainder. So this is going
to be 7 times 49. And we know that 49 is the
same thing as 7 times 7. So how can we rewrite this? This is the same thing
as taking the cube root of negative 1
times 7 times 7 times 7, which is the same
thing as taking the cube root of negative 1 times the
cube root of 7 times 7 times 7. Now, what's the cube
root of negative 1? Well, negative 1 times itself
three times is negative 1. So this right here
is negative 1. You could verify it. Negative 1 times negative
1 times negative 1 is indeed negative 1. This becomes positive 1. Multiply by negative 1
again, you get negative 1. So this is negative 1. And then this over here,
the cube root of 7 times 7 times 7-- well, that's
just going to be 7. 7 multiplied by
itself three times gives us 7 times
7 times 7 or 343. So it's going to
be negative 1 times 7, which is the same
thing as negative 7. So our answer is negative 7. And we're done.