Simplify square root of 39y^9

$\sqrt{39 y^{9}}$

Step 1

Rewrite $39 y^{9}$ as ${({(y^{2})}^{2})}^{2} \cdot (39 y)$ .

Factor out $y^{8}$ .

$\sqrt{39 (y^{8} y)}$

Rewrite $y^{8}$ as ${(y^{4})}^{2}$ .

$\sqrt{39 ({(y^{4})}^{2} y)}$

Reorder $39$ and ${(y^{4})}^{2}$ .

$\sqrt{{(y^{4})}^{2} \cdot 39 y}$

Rewrite $y^{4}$ as ${(y^{2})}^{2}$ .

$\sqrt{{({(y^{2})}^{2})}^{2} \cdot 39 y}$

Add parentheses.

$\sqrt{{({(y^{2})}^{2})}^{2} \cdot (39 y)}$

Step 2

Pull terms out from under the radical.

${(y^{2})}^{2} \sqrt{39 y}$

Step 3

Multiply the exponents in ${(y^{2})}^{2}$ .

Apply the power rule and multiply exponents, ${(a^{m})}^{n} = a^{m n}$ .

$y^{2 \cdot 2} \sqrt{39 y}$

Multiply $2$ by $2$ .

$y^{4} \sqrt{39 y}$