How do you simplify sqrt(32/4)324?

1 Answer
Jan 29, 2016

2sqrt222

Explanation:

There are 2 solutions :)

The first solution is:

Since sqrt(a/b) = sqrt(a)/sqrt(b)ab=ab, where bb is not equal to 00.

First we simplify the numerator, since there is no exact value of sqrt3232 we take its perfect squares. 1616 is a perfect square since 4*4 = 1644=16. Dividing 3232 by 1616, we get 16 * 2 = 32162=32, therefore:

sqrt32 = sqrt16*sqrt2 32=162
= 4sqrt2=42

Since now we're done in the numerator, we're gonna simplify the denominator, since 44 is perfect square, 4 = 2 * 24=22, the sqrt44 is equal to 22.

Plugging all the answers, we get:

(4sqrt2)/2422

since 44 and 22 is a whole number, we can divide these 2 whole numbers, we get:

2sqrt222

this is the final answer :)

the 2nd solution is:

First we simply evaluate the fraction inside the radical sign (square root)

sqrt(32/4) = sqrt(8)324=8

since, 32/4324 = 88, then we get sqrt88

sqrt8 = sqrt4*sqrt28=42

= 2sqrt2=22