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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.

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

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

Evaluate the exponent.

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

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

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

Step 5

The result can be shown in multiple forms.

Exact Form:

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

Decimal Form:

$0.13245323 \dots$

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