Question

6th period alg 2
5-1 radicals/roots
find the cube root.
\\(\sqrt3{-64x^{18}}\\)
select the correct choice below and, if necessary, fill in the answer box to complete your choice.
\\(\bigcirc\\) a. \\(\sqrt3{-64x^{18}} = \square\\)
\\(\bigcirc\\) b. the cube root is not a real number.

Explanation:

Step1: Analyze the cube root of -64

We know that \((-4)^3=-64\), so \(\sqrt[3]{-64} = -4\).

Step2: Analyze the cube root of \(x^{18}\)

Using the property \(\sqrt[n]{a^m}=a^{\frac{m}{n}}\), for \(\sqrt[3]{x^{18}}\), we have \(x^{\frac{18}{3}}=x^6\).

Step3: Combine the two results

Since \(\sqrt[3]{-64x^{18}}=\sqrt[3]{-64}\times\sqrt[3]{x^{18}}\), substituting the results from Step1 and Step2, we get \(-4\times x^6=-4x^6\).

Answer:

A. \(\sqrt[3]{-64x^{18}}=-4x^6\)