Question

select the correct answer.
which expression is equivalent to $3\sqrt{2y^3} \cdot 7\sqrt{18y}$ if $y > 0$?

a. $21y\sqrt{20y}$
b. $21y^2\sqrt{6y}$
c. $63y\sqrt{2y}$
d. $126y^2$

Explanation:

Step1: Multiply coefficients and radicals

$3 \times 7 \times \sqrt{2y^3 \times 18y}$

Step2: Simplify the product inside radical

$21 \times \sqrt{36y^4}$

Step3: Simplify the square root

$21 \times 6y^2$

Step4: Calculate final product

$21 \times 6y^2 = 126y^2$

Answer:

D. $126y^2$