How do you simplify $sqrt(128c^6)$ ?

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Answer 1 · 2016-04-23T23:07:01

$sqrt(128c^6) = 8abs(c)^3sqrt(2)$

Note that if $x >= 0$ then $sqrt(x)$ denotes the non-negative square root of $x$ .

So for any Real number $x$ we find:

$sqrt(x^2) = sqrt(abs(x)^2) = abs(x)$

If at least one of $a, b >= 0$ then:

$sqrt(ab) = sqrt(a)sqrt(b)$

So:

$sqrt(128c^6) = sqrt(2*64c^6) = sqrt(2*(8abs(c)^3)^2) = 8abs(c)^3sqrt(2)$

How do you simplify sqrt(128c^6)sqrt(128c^6)?