Question

Trying to understand how sqrt(27x^8) becomes 3^3/2 X^4

Answer 1

the square root is just like raising to the power of 1/2.
so sqrt(27x^8) becomes
(27x^8)^1/2
27 = 3^3, so:
(3^3 * x^8)^1/2
and then for a power raised to a power, you multiply the exponents:
3^(3*1/2) * x^ (8*1/2)
and get
3^(3/2) * x^4

Answer 2

sqrt(27) = sqrt(9*3) = sqrt(9)*sqrt(3) = 3*sqrt(3)


sqrt(x^8) =sqrt((x^4)^2) = x^4


So the answer is 3x^4*sqrt(3)

Answer 3

and

\[3 \sqrt{3} = 3 \times 3^{\frac{1}{2}} = 3^{1+\frac{1}{2}} = 3^{\frac{3}{2}}\]