How do you simplify $1/3sqrt252$ ?

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Answer 1 · 2015-11-07T13:05:42

$1/3 sqrt(252) = 2 sqrt(7)$

If $a, b >= 0$ then $sqrt(ab) = sqrt(a)sqrt(b)$

$252 = 2^2*3^2*7$

So:

$1/3 sqrt(252) = 1/3 sqrt(2^2 * 3^2 * 7) = 1/3 sqrt(2^2 * 3^2) sqrt(7)$

$= 1/3 sqrt((2 * 3)^2) sqrt(7) = 1/3*2*3*sqrt(7) = 2sqrt(7)$

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