Question

simplify. assume v is greater than or equal to zero.
$7\sqrt{27v^{5}}$

Explanation:

Step1: Factor radicand into perfect squares

$27v^5 = 9 \cdot 3 \cdot v^4 \cdot v = 3^2 \cdot (v^2)^2 \cdot 3v$

Step2: Simplify the square root

$\sqrt{3^2 \cdot (v^2)^2 \cdot 3v} = 3v^2\sqrt{3v}$

Step3: Multiply by the leading coefficient

$7 \cdot 3v^2\sqrt{3v}$

Answer:

$21v^2\sqrt{3v}$