how do i do this?

Question

Express your answer in simplified radical form
(square root of 108)
____
V108

Answer 1

108 doesn't have a nice, integral square root, but the teacher doesn't want you to reach for a calculator. You're supposed to apply this property of square roots:

√(a∙b) = (√a)(√b)

and you need to factor 108 into primes first: 108=2∙2∙3∙3∙3
So, √(108) = √(2∙2) ∙ √(3∙3) ∙ √3
= 2∙3∙√3
= 6√3

Answer 2

First, you should determine what numbers are factors at 108 (numbers that multiply to equal 108.) Well, you should find that 36 * 3 = 108. So, now, your sqrt(108) can be written as sqrt(36*8). We know what the square root of 36 is don't we? In fact, it is 6. So, we remove the 36 from the square root to get 6*sqrt(3).

I hope this was clear enough. I'm not sure what grade you are in.

Answer 3

Split 108 into it's prime numbers:
108/2 = 54
54/2 = 27
27/3 = 9
9/3 = 3
3/3 = 1
Therefore 108 = 2*2*3*3*3

Square root means same # multiplied by same #.

Out of 2*2*3*3*3, there is two 2s and three 3s. That means you can take out two 2s and two 3s.

sqrt (108) = sqrt (2*2*3*3*3) = 2 * sqrt(3*3*3) = (2*3) * sqrt (3)

answer = 6 * sqrt (3)

Answer 4

4 square root of 6

Answer 5

root (108) is equivalent to
root (27 * 4) writing this another way
root (27) * root (4) or
2 * root (27), now
root (27) is equivalent to
root (9) * root (3), which is
3 * root (3)
so 2 * 3 * root (3) is
6 root (3)

Answer 6

sqrt of 108

sqrt of 36 * sqrt of 3

6 sqrt of 3

Answer 7

get a calculater. The answer is 10.39230485

Hope this helps:p

Answer 8

_______
v (36)(3)

____
6 v3