Question

question 1 of 5

select the correct answer.

what is \\(\sqrt{f^5 g^{12}}\\) in simplest form?

\\(\bigcirc\\) \\(f^5 g^6\\)
\\(\bigcirc\\) \\(f^4 g^{11} \sqrt{fg}\\)
\\(\bigcirc\\) \\(f^2 g^4 \sqrt{fg^3}\\)
\\(\bigcirc\\) \\(f^2 g^6 \sqrt{f}\\)

Explanation:

⚡ Using what you learned: Roots and Radicals

Step 1: Split the radical

$$ \sqrt{f^5 g^{12}} = \sqrt{f^5} \cdot \sqrt{g^{12}} $$

Step 2: Simplify each part

Rewrite \( f^5 \) using the largest even power:

$$ \sqrt{f^5} = \sqrt{f^4 \cdot f} = f^2 \sqrt{f} $$

Simplify the even power of \( g \):

$$ \sqrt{g^{12}} = g^6 $$

Step 3: Combine the simplified terms

$$ f^2 \sqrt{f} \cdot g^6 = f^2 g^6 \sqrt{f} $$

Answer:

\( f^2 g^6 \sqrt{f} \) (the fourth option)