Basic Math Examples

\sqrt{\frac{6}{19}}

$\sqrt{\frac{6}{19}}$

Step 1

Rewrite

\sqrt{\frac{6}{19}}

$\sqrt{\frac{6}{19}}$ as

\frac{\sqrt{6}}{\sqrt{19}}

$\frac{\sqrt{6}}{\sqrt{19}}$ .

\frac{\sqrt{6}}{\sqrt{19}}

$\frac{\sqrt{6}}{\sqrt{19}}$

Step 2

Multiply

\frac{\sqrt{6}}{\sqrt{19}}

$\frac{\sqrt{6}}{\sqrt{19}}$ by

\frac{\sqrt{19}}{\sqrt{19}}

$\frac{\sqrt{19}}{\sqrt{19}}$ .

\frac{\sqrt{6}}{\sqrt{19}} \cdot \frac{\sqrt{19}}{\sqrt{19}}

$\frac{\sqrt{6}}{\sqrt{19}} \cdot \frac{\sqrt{19}}{\sqrt{19}}$

Step 3

Combine and simplify the denominator.

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Step 3.1

Multiply

\frac{\sqrt{6}}{\sqrt{19}}

$\frac{\sqrt{6}}{\sqrt{19}}$ by

\frac{\sqrt{19}}{\sqrt{19}}

$\frac{\sqrt{19}}{\sqrt{19}}$ .

\frac{\sqrt{6} \sqrt{19}}{\sqrt{19} \sqrt{19}}

$\frac{\sqrt{6} \sqrt{19}}{\sqrt{19} \sqrt{19}}$

Step 3.2

Raise

\sqrt{19}

$\sqrt{19}$ to the power of

1

$1$ .

\frac{\sqrt{6} \sqrt{19}}{{\sqrt{19}}^{1} \sqrt{19}}

$\frac{\sqrt{6} \sqrt{19}}{{\sqrt{19}}^{1} \sqrt{19}}$

Step 3.3

Raise

\sqrt{19}

$\sqrt{19}$ to the power of

1

$1$ .

\frac{\sqrt{6} \sqrt{19}}{{\sqrt{19}}^{1} {\sqrt{19}}^{1}}

$\frac{\sqrt{6} \sqrt{19}}{{\sqrt{19}}^{1} {\sqrt{19}}^{1}}$

Step 3.4

Use the power rule

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

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

\frac{\sqrt{6} \sqrt{19}}{{\sqrt{19}}^{1 + 1}}

$\frac{\sqrt{6} \sqrt{19}}{{\sqrt{19}}^{1 + 1}}$

Step 3.5

Add

1

$1$ and

1

$1$ .

\frac{\sqrt{6} \sqrt{19}}{{\sqrt{19}}^{2}}

$\frac{\sqrt{6} \sqrt{19}}{{\sqrt{19}}^{2}}$

Step 3.6

Rewrite

{\sqrt{19}}^{2}

${\sqrt{19}}^{2}$ as

19

$19$ .

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Step 3.6.1

Use

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

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

\sqrt{19}

$\sqrt{19}$ as

19^{\frac{1}{2}}

$19^{\frac{1}{2}}$ .

\frac{\sqrt{6} \sqrt{19}}{{(19^{\frac{1}{2}})}^{2}}

$\frac{\sqrt{6} \sqrt{19}}{{(19^{\frac{1}{2}})}^{2}}$

Step 3.6.2

Apply the power rule and multiply exponents,

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

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

\frac{\sqrt{6} \sqrt{19}}{19^{\frac{1}{2} \cdot 2}}

$\frac{\sqrt{6} \sqrt{19}}{19^{\frac{1}{2} \cdot 2}}$

Step 3.6.3

Combine

\frac{1}{2}

$\frac{1}{2}$ and

$2$ .

$\frac{\sqrt{6} \sqrt{19}}{19^{\frac{2}{2}}}$

Step 3.6.4

Cancel the common factor of

$2$ .

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Step 3.6.4.1

Cancel the common factor.

$\frac{\sqrt{6} \sqrt{19}}{19^{\frac{2}{2}}}$

Step 3.6.4.2

Rewrite the expression.

$\frac{\sqrt{6} \sqrt{19}}{19^{1}}$

Step 3.6.5

Evaluate the exponent.

$\frac{\sqrt{6} \sqrt{19}}{19}$

Step 4

Simplify the numerator.

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Step 4.1

Combine using the product rule for radicals.

$\frac{\sqrt{6 \cdot 19}}{19}$

Step 4.2

Multiply

$6$ by

$19$ .

$\frac{\sqrt{114}}{19}$

Step 5

The result can be shown in multiple forms.

Exact Form:

$\frac{\sqrt{114}}{19}$

Decimal Form:

$0.56195148 \dots$