Question

question 2 of 5

select the correct answer.

what is \\(\sqrt{150x^3y}\\) in simplest form?

\\(5x\sqrt{6xy}\\)

\\(6xy\sqrt{5x^2}\\)

\\(25x^2\sqrt{6xy}\\)

\\(5\sqrt{6x^3y}\\)

Explanation:

⚡ Using what you learned: simplifying radical expressions

Step 1: Factor the numerical coefficient

Find the largest perfect square factor of \( 150 \):

$$ 150 = 25 \times 6 $$

Step 2: Factor the variable terms

Identify the perfect square parts of the variables under the square root:

$$ x^3 = x^2 \times x $$

$$ y = y $$

Step 3: Group perfect squares and simplify

Group the perfect squares together and simplify the radical:

$$ \sqrt{150x^3y} = \sqrt{25 \cdot 6 \cdot x^2 \cdot x \cdot y} $$

$$ \sqrt{150x^3y} = \sqrt{25x^2} \cdot \sqrt{6xy} $$

$$ \sqrt{150x^3y} = 5x\sqrt{6xy} $$

Answer:

\( 5x\sqrt{6xy} \) (the first option)