Question

Radical (108x^5y^8)/Radical 6xy^5. simplest form.

Answer 1

Hello, do you know the first step?

Answer 2

no

Answer 3

You want to simplify your unfactorable temrs. What are the factors of 108 and 6?

Answer 4

18

Answer 5

18 and?

Answer 6

6

Answer 7

Okay, so we have 6 and 18. Can those also be factored?

Answer 8

6 and 3

Answer 9

Okay, so factors of 18 are 6 and 3.

Can 6 be factored more?

Answer 10

2 and 3

Answer 11

Alright, so we want to then take all of our prime factors of 108 (The temrs that CANNOT be factored more) and if we have two of them, we put them on the outside of the radical
\[\sqrt{3 + 3 + 2x^5y^8} = 3 \sqrt{2x^5y^8}\]

Basically, the reason we look for two of the same terms and put them on the outisde is because any two same square roots multiplied by each other will always be the number itself. For example, \[\sqrt{2} * \sqrt{2} = 2\] We put them on the outside to simplify the inside of the radical. Does that make sense?

Answer 12

yes

Answer 13

But I think we got our factors wrong

108 = 6 * 18

Now the factors of six are: 3 * 2 (Prime factors)

6 * 3 (3 is another primse factor)
3 * 2(Another primse factor
So we have. \[\sqrt{3 * 2 * 3 * 3 * 2x^5y^8}\]

Now can you take two pairs of each number and put them on the outisde?

Answer 14

3 & 2

Answer 15

We have 3 3s and 2 2s. So we keep 1 three inside. \[6 \sqrt{3x^5y^8} \]

Now you want to do the same thing to the x and y temrs. I'll make it simpler. \[6 \sqrt{3x * x * x * x * x * x * y * y * y * y * y * y * y * y}\]
Now take each two sets of x and two sets of y and put them on the outside, too.