Simplify (3y^2)/( square root of 20y^5)

$\frac{3 y^{2}}{\sqrt{20 y^{5}}}$

Simplify the denominator.

Rewrite $20 y^{5}$ as ${(2 y^{2})}^{2} \cdot (5 y)$ .

Factor $4$ out of $20$ .

$\frac{3 y^{2}}{\sqrt{4 (5) y^{5}}}$

Rewrite $4$ as $2^{2}$ .

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

Factor out $y^{4}$ .

$\frac{3 y^{2}}{\sqrt{2^{2} \cdot 5 (y^{4} y)}}$

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

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

Move $5$ .

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

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

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

Add parentheses.

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

Pull terms out from under the radical.

$\frac{3 y^{2}}{2 y^{2} \sqrt{5 y}}$

Cancel the common factor of $y^{2}$ .

Cancel the common factor.

$\frac{3 y^{2}}{2 y^{2} \sqrt{5 y}}$

Rewrite the expression.

$\frac{3}{2 \sqrt{5 y}}$

Multiply $\frac{3}{2 \sqrt{5 y}}$ by $\frac{\sqrt{5 y}}{\sqrt{5 y}}$ .

$\frac{3}{2 \sqrt{5 y}} \cdot \frac{\sqrt{5 y}}{\sqrt{5 y}}$

Combine and simplify the denominator.

Multiply $\frac{3}{2 \sqrt{5 y}}$ by $\frac{\sqrt{5 y}}{\sqrt{5 y}}$ .

$\frac{3 \sqrt{5 y}}{2 \sqrt{5 y} \sqrt{5 y}}$

Move $\sqrt{5 y}$ .

$\frac{3 \sqrt{5 y}}{2 (\sqrt{5 y} \sqrt{5 y})}$

Raise $\sqrt{5 y}$ to the power of $1$ .

$\frac{3 \sqrt{5 y}}{2 ({\sqrt{5 y}}^{1} \sqrt{5 y})}$

Raise $\sqrt{5 y}$ to the power of $1$ .

$\frac{3 \sqrt{5 y}}{2 ({\sqrt{5 y}}^{1} {\sqrt{5 y}}^{1})}$

Use the power rule $a^{m} a^{n} = a^{m + n}$ to combine exponents.

$\frac{3 \sqrt{5 y}}{2 {\sqrt{5 y}}^{1 + 1}}$

Add $1$ and $1$ .

$\frac{3 \sqrt{5 y}}{2 {\sqrt{5 y}}^{2}}$

Rewrite ${\sqrt{5 y}}^{2}$ as $5 y$ .

Use $\sqrt[n]{a^{x}} = a^{\frac{x}{n}}$ to rewrite $\sqrt{5 y}$ as ${(5 y)}^{\frac{1}{2}}$ .

$\frac{3 \sqrt{5 y}}{2 {({(5 y)}^{\frac{1}{2}})}^{2}}$

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

$\frac{3 \sqrt{5 y}}{2 {(5 y)}^{\frac{1}{2} \cdot 2}}$

Combine $\frac{1}{2}$ and $2$ .

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

Cancel the common factor of $2$ .

Cancel the common factor.

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

Rewrite the expression.

$\frac{3 \sqrt{5 y}}{2 {(5 y)}^{1}}$

Simplify.

$\frac{3 \sqrt{5 y}}{2 (5 y)}$

Multiply $2$ by $5$ .

$\frac{3 \sqrt{5 y}}{10 y}$

Simplify (3y^2)/( square root of 20y^5)

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