Perform the multiplication. The variable represents a positive number. $(\sqrt{125 y})\left(\sqrt{5 y^{7}}\right)$

Question

Quizplus · Accepted Answer

When we multiply the two square roots with the same base, we add their exponents. Hence, $\sqrt{125 y} = \sqrt{5^3y}=\sqrt{5^2\cdot5y}=5\sqrt{5y}$ and $\sqrt{5y^7}=y^3 \sqrt{5y}$. Multiplying these, we get $5\sqrt{5y}\cdot y^3 \sqrt{5y} = 5y^3 \cdot 5\sqrt{y} = 25y^3\sqrt{y} = \sqrt{(25y^6) \cdot (5y)} = \sqrt{125y^7}$. Thus, the answer is $\boxed{	extbf{(C) }25y\sqrt{y}}$.

Perform the Multiplication (125y)(5y7)(\sqrt{125 y})\left(\sqrt{5 y^{7}}\right)(125y​)(5y7​) A)25 Y B)5 Y 4 C)25 Y 4 D)5 Y

Perform the Multiplication $(\sqrt{125 y})\left(\sqrt{5 y^{7}}\right)$ A)25 Y
B)5 Y ⁴
C)25 Y ⁴
D)5 Y