There are 2 solutions :)
The first solution is:
Since sqrt(a/b) = sqrt(a)/sqrt(b)√ab=√a√b, where bb is not equal to 00.
First we simplify the numerator, since there is no exact value of sqrt32√32 we take its perfect squares. 1616 is a perfect square since 4*4 = 164⋅4=16. Dividing 3232 by 1616, we get 16 * 2 = 3216⋅2=32, therefore:
sqrt32 = sqrt16*sqrt2 √32=√16⋅√2
= 4sqrt2=4√2
Since now we're done in the numerator, we're gonna simplify the denominator, since 44 is perfect square, 4 = 2 * 24=2⋅2, the sqrt4√4 is equal to 22.
Plugging all the answers, we get:
(4sqrt2)/24√22
since 44 and 22 is a whole number, we can divide these 2 whole numbers, we get:
2sqrt22√2
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 sqrt8√8
sqrt8 = sqrt4*sqrt2√8=√4⋅√2
= 2sqrt2=2√2