How do you simplify $sqrt(32a^7b^4 )$ ?

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Answer 1 · 2015-10-09T16:41:16

$4a^3b^2sqrt(2a)$

Since everything under the square root is being multiplied, we can take out things that are squares. Let's break things up one piece at a time:

The $a$ variable:

$sqrt(a^7)$
$a^6*a = a^7$
$a^3sqrt(a) = sqrt(a^7)$

The $b$ variable:

$sqrt(b^4)$
$b^2 = sqrt(b^4)$

The constant (32):

$sqrt(16*2) = sqrt(32)$
$4sqrt(2) = sqrt(32)$

Now we multiply everything together in order to get our answer.
$4a^3b^2sqrt(2a)$

How do you simplify sqrt(32a^7b^4 )sqrt(32a^7b^4 )?