Examples

\sqrt{\frac{5 x}{7}}

$\sqrt{\frac{5 x}{7}}$

Step 1

Rewrite

\sqrt{\frac{5 x}{7}}

$\sqrt{\frac{5 x}{7}}$ as

\frac{\sqrt{5 x}}{\sqrt{7}}

$\frac{\sqrt{5 x}}{\sqrt{7}}$ .

\frac{\sqrt{5 x}}{\sqrt{7}}

$\frac{\sqrt{5 x}}{\sqrt{7}}$

Step 2

Multiply

\frac{\sqrt{5 x}}{\sqrt{7}}

$\frac{\sqrt{5 x}}{\sqrt{7}}$ by

\frac{\sqrt{7}}{\sqrt{7}}

$\frac{\sqrt{7}}{\sqrt{7}}$ .

\frac{\sqrt{5 x}}{\sqrt{7}} \cdot \frac{\sqrt{7}}{\sqrt{7}}

$\frac{\sqrt{5 x}}{\sqrt{7}} \cdot \frac{\sqrt{7}}{\sqrt{7}}$

Step 3

Combine and simplify the denominator.

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Step 3.1

Multiply

\frac{\sqrt{5 x}}{\sqrt{7}}

$\frac{\sqrt{5 x}}{\sqrt{7}}$ by

\frac{\sqrt{7}}{\sqrt{7}}

$\frac{\sqrt{7}}{\sqrt{7}}$ .

\frac{\sqrt{5 x} \sqrt{7}}{\sqrt{7} \sqrt{7}}

$\frac{\sqrt{5 x} \sqrt{7}}{\sqrt{7} \sqrt{7}}$

Step 3.2

Raise

\sqrt{7}

$\sqrt{7}$ to the power of

1

$1$ .

\frac{\sqrt{5 x} \sqrt{7}}{{\sqrt{7}}^{1} \sqrt{7}}

$\frac{\sqrt{5 x} \sqrt{7}}{{\sqrt{7}}^{1} \sqrt{7}}$

Step 3.3

Raise

\sqrt{7}

$\sqrt{7}$ to the power of

1

$1$ .

\frac{\sqrt{5 x} \sqrt{7}}{{\sqrt{7}}^{1} {\sqrt{7}}^{1}}

$\frac{\sqrt{5 x} \sqrt{7}}{{\sqrt{7}}^{1} {\sqrt{7}}^{1}}$

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{5 x} \sqrt{7}}{{\sqrt{7}}^{1 + 1}}

$\frac{\sqrt{5 x} \sqrt{7}}{{\sqrt{7}}^{1 + 1}}$

Step 3.5

Add

1

$1$ and

1

$1$ .

\frac{\sqrt{5 x} \sqrt{7}}{{\sqrt{7}}^{2}}

$\frac{\sqrt{5 x} \sqrt{7}}{{\sqrt{7}}^{2}}$

Step 3.6

Rewrite

{\sqrt{7}}^{2}

${\sqrt{7}}^{2}$ as

7

$7$ .

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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{7}

$\sqrt{7}$ as

7^{\frac{1}{2}}

$7^{\frac{1}{2}}$ .

\frac{\sqrt{5 x} \sqrt{7}}{{(7^{\frac{1}{2}})}^{2}}

$\frac{\sqrt{5 x} \sqrt{7}}{{(7^{\frac{1}{2}})}^{2}}$

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{5 x} \sqrt{7}}{7^{\frac{1}{2} \cdot 2}}

$\frac{\sqrt{5 x} \sqrt{7}}{7^{\frac{1}{2} \cdot 2}}$

Step 3.6.3

Combine

\frac{1}{2}

$\frac{1}{2}$ and

2

$2$ .

\frac{\sqrt{5 x} \sqrt{7}}{7^{\frac{2}{2}}}

$\frac{\sqrt{5 x} \sqrt{7}}{7^{\frac{2}{2}}}$

Step 3.6.4

Cancel the common factor of

2

$2$ .

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Step 3.6.4.1

Cancel the common factor.

$\frac{\sqrt{5 x} \sqrt{7}}{7^{\frac{2}{2}}}$

Step 3.6.4.2

Rewrite the expression.

$\frac{\sqrt{5 x} \sqrt{7}}{7^{1}}$

Step 3.6.5

Evaluate the exponent.

$\frac{\sqrt{5 x} \sqrt{7}}{7}$

Step 4

Simplify the numerator.

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Step 4.1

Combine using the product rule for radicals.

$\frac{\sqrt{5 x \cdot 7}}{7}$

Step 4.2

Multiply

$7$ by

$5$ .

$\frac{\sqrt{35 x}}{7}$

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