Question

select the correct answer.

what is \\(\sqrt{144x^2y^5}\\) in simplest form?

\\(\bigcirc\\ xy^2\sqrt{144y}\\)
\\(\bigcirc\\ 72xy^2\sqrt{y}\\)
\\(\bigcirc\\ 12xy\sqrt{xy^4}\\)
\\(\bigcirc\\ 12xy^2\sqrt{y}\\)

Explanation:

⚡ Using what you learned: simplifying radical expressions

Step 1: Separate the radical

$$ \sqrt{144x^2y^5} = \sqrt{144} \cdot \sqrt{x^2} \cdot \sqrt{y^5} $$

Step 2: Simplify each part

$$ \sqrt{144} = 12 $$

$$ \sqrt{x^2} = x $$

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

Step 3: Combine the simplified terms

$$ 12 \cdot x \cdot y^2\sqrt{y} = 12xy^2\sqrt{y} $$

Answer:

\( 12xy^2\sqrt{y} \) (the fourth option)