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

1 Answer
Apr 23, 2016

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

Explanation:

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)