Simplify square root of 1/57

$\sqrt{\frac{1}{57}}$

Step 1

Rewrite $\sqrt{\frac{1}{57}}$ as $\frac{\sqrt{1}}{\sqrt{57}}$ .

$\frac{\sqrt{1}}{\sqrt{57}}$

Step 2

Any root of $1$ is $1$ .

$\frac{1}{\sqrt{57}}$

Step 3

Multiply $\frac{1}{\sqrt{57}}$ by $\frac{\sqrt{57}}{\sqrt{57}}$ .

$\frac{1}{\sqrt{57}} \cdot \frac{\sqrt{57}}{\sqrt{57}}$

Step 4

Combine and simplify the denominator.

Multiply $\frac{1}{\sqrt{57}}$ by $\frac{\sqrt{57}}{\sqrt{57}}$ .

$\frac{\sqrt{57}}{\sqrt{57} \sqrt{57}}$

Raise $\sqrt{57}$ to the power of $1$ .

$\frac{\sqrt{57}}{{\sqrt{57}}^{1} \sqrt{57}}$

Raise $\sqrt{57}$ to the power of $1$ .

$\frac{\sqrt{57}}{{\sqrt{57}}^{1} {\sqrt{57}}^{1}}$

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

$\frac{\sqrt{57}}{{\sqrt{57}}^{1 + 1}}$

Add $1$ and $1$ .

$\frac{\sqrt{57}}{{\sqrt{57}}^{2}}$

Rewrite ${\sqrt{57}}^{2}$ as $57$ .

Use $\sqrt[n]{a^{x}} = a^{\frac{x}{n}}$ to rewrite $\sqrt{57}$ as $57^{\frac{1}{2}}$ .

$\frac{\sqrt{57}}{{(57^{\frac{1}{2}})}^{2}}$

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

$\frac{\sqrt{57}}{57^{\frac{1}{2} \cdot 2}}$

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

$\frac{\sqrt{57}}{57^{\frac{2}{2}}}$

Cancel the common factor of $2$ .

Cancel the common factor.

$\frac{\sqrt{57}}{57^{\frac{2}{2}}}$

Rewrite the expression.

$\frac{\sqrt{57}}{57^{1}}$

Evaluate the exponent.

$\frac{\sqrt{57}}{57}$

Step 5

The result can be shown in multiple forms.

Exact Form:

$\frac{\sqrt{57}}{57}$

Decimal Form:

$0.13245323 \dots$