Question

slide the red circle in front of correct answer.

1. which expression is equivalent to \\(\sqrt{20x^{16}y^{25}}\\) for positive x and y values?

a \\(2x^4y^5\sqrt{5}\\)
b \\(5x^4y^5\sqrt{2}\\)
c \\(2x^8y^{12}\sqrt{5y}\\)
d \\(5x^8y^{12}\sqrt{2y}\\)

Explanation:

Step1: Factor the radicand

$\sqrt{20x^{16}y^{25}} = \sqrt{4 \times 5 \times x^{16} \times y^{24} \times y}$

Step2: Simplify perfect squares

$\sqrt{4} = 2$, $\sqrt{x^{16}} = x^8$, $\sqrt{y^{24}} = y^{12}$; remaining: $\sqrt{5y}$

Step3: Combine simplified terms

$2x^8y^{12}\sqrt{5y}$ (Note: Check options—corrected typo in C: should be $2x^8y^{12}\sqrt{5y}$)

Answer:

C. $2x^8y^{12}\sqrt{5y}$