Basic Math Examples

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

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

Step 1

Rewrite

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

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

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

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

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

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

Step 2

Any root of

1

$1$ is

1

$1$ .

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

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

Step 3

Multiply

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

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

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

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

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

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

Step 4

Combine and simplify the denominator.

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Step 4.1

Multiply

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

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

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

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

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

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

Step 4.2

Raise

\sqrt{57}

$\sqrt{57}$ to the power of

1

$1$ .

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

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

Step 4.3

Raise

\sqrt{57}

$\sqrt{57}$ to the power of

1

$1$ .

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

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

Step 4.4

Use the power rule

a^{m} a^{n} = a^{m + n}

$a^{m} a^{n} = a^{m + n}$ to combine exponents.

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

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

Step 4.5

Add

1

$1$ and

1

$1$ .

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

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

Step 4.6

Rewrite

{\sqrt{57}}^{2}

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

57

$57$ .

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Step 4.6.1

Use

\sqrt[n]{a^{x}} = a^{\frac{x}{n}}

$\sqrt[n]{a^{x}} = a^{\frac{x}{n}}$ to rewrite

\sqrt{57}

$\sqrt{57}$ as

57^{\frac{1}{2}}

$57^{\frac{1}{2}}$ .

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

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

Step 4.6.2

Apply the power rule and multiply exponents,

{(a^{m})}^{n} = a^{m n}

${(a^{m})}^{n} = a^{m n}$ .

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

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

Step 4.6.3

Combine

\frac{1}{2}

$\frac{1}{2}$ and

2

$2$ .

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

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

Step 4.6.4

Cancel the common factor of

2

$2$ .

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Step 4.6.4.1

Cancel the common factor.

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

Step 4.6.4.2

Rewrite the expression.

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

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

Step 4.6.5

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:

$0.13245323 \dots$

$[\begin{array}{c} x^{2} & \frac{1}{2} \\ \sqrt{π} & \int x d x \end{array}]$