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Simplify square root of 75y^7

$\sqrt{75 y^{7}}$

Step 1

Rewrite $75 y^{7}$ as ${(5 y^{3})}^{2} \cdot (3 y)$ .

Factor $25$ out of $75$ .

$\sqrt{25 (3) y^{7}}$

Rewrite $25$ as $5^{2}$ .

$\sqrt{5^{2} \cdot 3 y^{7}}$

Factor out $y^{6}$ .

$\sqrt{5^{2} \cdot 3 (y^{6} y)}$

Rewrite $y^{6}$ as ${(y^{3})}^{2}$ .

$\sqrt{5^{2} \cdot 3 ({(y^{3})}^{2} y)}$

Move $3$ .

$\sqrt{5^{2} {(y^{3})}^{2} \cdot 3 y}$

Rewrite $5^{2} {(y^{3})}^{2}$ as ${(5 y^{3})}^{2}$ .

$\sqrt{{(5 y^{3})}^{2} \cdot 3 y}$

Add parentheses.

$\sqrt{{(5 y^{3})}^{2} \cdot (3 y)}$

$\sqrt{{(5 y^{3})}^{2} \cdot (3 y)}$

Step 2

Pull terms out from under the radical.

$5 y^{3} \sqrt{3 y}$

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