Question

algebra 4: 6(a) (lms)
5-1 nth roots, radicals and rationa
find the cube root.
\\(\sqrt3{-64x^9}\\)
select the correct choice below and, if necessary, fill in the answer bo
a. \\(\sqrt3{-64x^9} = \square\\)
b. the cube root is not a real number.

Explanation:

Step1: Split radical into two parts

$\sqrt[3]{-64x^9} = \sqrt[3]{-64} \cdot \sqrt[3]{x^9}$

Step2: Compute cube root of -64

$\sqrt[3]{-64} = -4$, since $(-4)^3 = -64$

Step3: Compute cube root of $x^9$

$\sqrt[3]{x^9} = x^{\frac{9}{3}} = x^3$

Step4: Multiply the two results

$-4 \cdot x^3 = -4x^3$

Answer:

A. $\sqrt[3]{-64x^9} = -4x^3$