Simplify (4y^3)/( square root of 20y^2)

$\frac{4 y^{3}}{\sqrt{20 y^{2}}}$

Step 1

Simplify the denominator.

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

Factor $4$ out of $20$ .

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

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

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

Move $5$ .

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

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

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

Pull terms out from under the radical.

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

Step 2

Reduce the expression by cancelling the common factors.

Cancel the common factor of $4$ and $2$ .

Factor $2$ out of $4 y^{3}$ .

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

Cancel the common factors.

Factor $2$ out of $2 y \sqrt{5}$ .

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

Cancel the common factor.

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

Rewrite the expression.

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

Cancel the common factor of $y^{3}$ and $y$ .

Factor $y$ out of $2 y^{3}$ .

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

Cancel the common factors.

Factor $y$ out of $y \sqrt{5}$ .

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

Cancel the common factor.

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

Rewrite the expression.

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

Step 3

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

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

Step 4

Combine and simplify the denominator.

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

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

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

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

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

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

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

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

Add $1$ and $1$ .

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

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

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

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

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

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

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

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

Cancel the common factor of $2$ .

Cancel the common factor.

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

Rewrite the expression.

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

Evaluate the exponent.

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

Simplify (4y^3)/( square root of 20y^2)

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