Simplify 5/( square root of 30)

$\frac{5}{\sqrt{30}}$

Step 1

Multiply $\frac{5}{\sqrt{30}}$ by $\frac{\sqrt{30}}{\sqrt{30}}$ .

$\frac{5}{\sqrt{30}} \cdot \frac{\sqrt{30}}{\sqrt{30}}$

Step 2

Combine and simplify the denominator.

Multiply $\frac{5}{\sqrt{30}}$ by $\frac{\sqrt{30}}{\sqrt{30}}$ .

$\frac{5 \sqrt{30}}{\sqrt{30} \sqrt{30}}$

Raise $\sqrt{30}$ to the power of $1$ .

$\frac{5 \sqrt{30}}{{\sqrt{30}}^{1} \sqrt{30}}$

Raise $\sqrt{30}$ to the power of $1$ .

$\frac{5 \sqrt{30}}{{\sqrt{30}}^{1} {\sqrt{30}}^{1}}$

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

$\frac{5 \sqrt{30}}{{\sqrt{30}}^{1 + 1}}$

Add $1$ and $1$ .

$\frac{5 \sqrt{30}}{{\sqrt{30}}^{2}}$

Rewrite ${\sqrt{30}}^{2}$ as $30$ .

Use $\sqrt[n]{a^{x}} = a^{\frac{x}{n}}$ to rewrite $\sqrt{30}$ as $30^{\frac{1}{2}}$ .

$\frac{5 \sqrt{30}}{{(30^{\frac{1}{2}})}^{2}}$

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

$\frac{5 \sqrt{30}}{30^{\frac{1}{2} \cdot 2}}$

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

$\frac{5 \sqrt{30}}{30^{\frac{2}{2}}}$

Cancel the common factor of $2$ .

Cancel the common factor.

$\frac{5 \sqrt{30}}{30^{\frac{2}{2}}}$

Rewrite the expression.

$\frac{5 \sqrt{30}}{30^{1}}$

Evaluate the exponent.

$\frac{5 \sqrt{30}}{30}$

Step 3

Cancel the common factor of $5$ and $30$ .

Factor $5$ out of $5 \sqrt{30}$ .

$\frac{5 (\sqrt{30})}{30}$

Cancel the common factors.

Factor $5$ out of $30$ .

$\frac{5 \sqrt{30}}{5 \cdot 6}$

Cancel the common factor.

$\frac{5 \sqrt{30}}{5 \cdot 6}$

Rewrite the expression.

$\frac{\sqrt{30}}{6}$

Step 4

The result can be shown in multiple forms.

Exact Form:

$\frac{\sqrt{30}}{6}$

Decimal Form:

$0.91287092 \dots$

Simplify 5/( square root of 30)

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