Pre-Algebra Examples

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

Step 1

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

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Step 1.1

Factor out $y^{8}$ .

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

Step 1.2

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

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

Step 1.3

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

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

Step 1.4

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

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

Step 1.5

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 ${(y^{2})}^{2}$ .

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Step 3.1

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

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

Step 3.2

Multiply $2$ by $2$ .

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