Simplify 10/(3 square root of 20)

$\frac{10}{3 \sqrt{20}}$

Step 1

Simplify the denominator.

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

Factor $4$ out of $20$ .

$\frac{10}{3 \sqrt{4 (5)}}$

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

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

Pull terms out from under the radical.

$\frac{10}{3 \cdot 2 \sqrt{5}}$

Multiply $3$ by $2$ .

$\frac{10}{6 \sqrt{5}}$

Step 2

Cancel the common factor of $10$ and $6$ .

Factor $2$ out of $10$ .

$\frac{2 (5)}{6 \sqrt{5}}$

Cancel the common factors.

Factor $2$ out of $6 \sqrt{5}$ .

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

Cancel the common factor.

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

Rewrite the expression.

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

Step 3

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

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

Step 4

Combine and simplify the denominator.

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

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

Move $\sqrt{5}$ .

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

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

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

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

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

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

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

Add $1$ and $1$ .

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

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

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

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

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

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

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

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

Cancel the common factor of $2$ .

Cancel the common factor.

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

Rewrite the expression.

$\frac{5 \sqrt{5}}{3 \cdot 5^{1}}$

Evaluate the exponent.

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

Step 5

Cancel the common factor of $5$ .

Cancel the common factor.

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

Rewrite the expression.

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

Step 6

The result can be shown in multiple forms.

Exact Form:

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

Decimal Form:

$0.74535599 \dots$

Simplify 10/(3 square root of 20)

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