Simplify (3r^3)/( square root of 20r)

$\frac{3 r^{3}}{\sqrt{20 r}}$

Step 1

Simplify the denominator.

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

Factor $4$ out of $20$ .

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

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

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

Add parentheses.

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

Pull terms out from under the radical.

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

Step 2

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

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

Step 3

Simplify terms.

Combine and simplify the denominator.

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

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

Move $\sqrt{5 r}$ .

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

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

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

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

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

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

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

Add $1$ and $1$ .

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

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

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

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

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

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

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

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

Cancel the common factor of $2$ .

Cancel the common factor.

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

Rewrite the expression.

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

Simplify.

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

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

Factor $r$ out of $3 r^{3} \sqrt{5 r}$ .

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

Cancel the common factors.

Factor $r$ out of $2 (5 r)$ .

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

Cancel the common factor.

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

Rewrite the expression.

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

Step 4

Multiply $2$ by $5$ .

$\frac{3 r^{2} \sqrt{5 r}}{10}$

Simplify (3r^3)/( square root of 20r)

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