Finite Math Examples

$\sqrt{\frac{175}{\sqrt{7}}}$

Step 1

Multiply $\frac{175}{\sqrt{7}}$ by $\frac{\sqrt{7}}{\sqrt{7}}$ .

$\sqrt{\frac{175}{\sqrt{7}} \cdot \frac{\sqrt{7}}{\sqrt{7}}}$

Step 2

Combine and simplify the denominator.

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Step 2.1

Multiply $\frac{175}{\sqrt{7}}$ by $\frac{\sqrt{7}}{\sqrt{7}}$ .

$\sqrt{\frac{175 \sqrt{7}}{\sqrt{7} \sqrt{7}}}$

Step 2.2

Raise $\sqrt{7}$ to the power of $1$ .

$\sqrt{\frac{175 \sqrt{7}}{{\sqrt{7}}^{1} \sqrt{7}}}$

Step 2.3

Raise $\sqrt{7}$ to the power of $1$ .

$\sqrt{\frac{175 \sqrt{7}}{{\sqrt{7}}^{1} {\sqrt{7}}^{1}}}$

Step 2.4

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

$\sqrt{\frac{175 \sqrt{7}}{{\sqrt{7}}^{1 + 1}}}$

Step 2.5

Add $1$ and $1$ .

$\sqrt{\frac{175 \sqrt{7}}{{\sqrt{7}}^{2}}}$

Step 2.6

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

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Step 2.6.1

Use $\sqrt[n]{a^{x}} = a^{\frac{x}{n}}$ to rewrite $\sqrt{7}$ as $7^{\frac{1}{2}}$ .

$\sqrt{\frac{175 \sqrt{7}}{{(7^{\frac{1}{2}})}^{2}}}$

Step 2.6.2

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

$\sqrt{\frac{175 \sqrt{7}}{7^{\frac{1}{2} \cdot 2}}}$

Step 2.6.3

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

$\sqrt{\frac{175 \sqrt{7}}{7^{\frac{2}{2}}}}$

Step 2.6.4

Cancel the common factor of $2$ .

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Step 2.6.4.1

Cancel the common factor.

$\sqrt{\frac{175 \sqrt{7}}{7^{\frac{2}{2}}}}$

Step 2.6.4.2

Rewrite the expression.

$\sqrt{\frac{175 \sqrt{7}}{7^{1}}}$

Step 2.6.5

Evaluate the exponent.

$\sqrt{\frac{175 \sqrt{7}}{7}}$

Step 3

Cancel the common factor of $175$ and $7$ .

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Step 3.1

Factor $7$ out of $175 \sqrt{7}$ .

$\sqrt{\frac{7 (25 \sqrt{7})}{7}}$

Step 3.2

Cancel the common factors.

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Step 3.2.1

Factor $7$ out of $7$ .

$\sqrt{\frac{7 (25 \sqrt{7})}{7 (1)}}$

Step 3.2.2

Cancel the common factor.

$\sqrt{\frac{7 (25 \sqrt{7})}{7 \cdot 1}}$

Step 3.2.3

Rewrite the expression.

$\sqrt{\frac{25 \sqrt{7}}{1}}$

Step 3.2.4

Divide $25 \sqrt{7}$ by $1$ .

$\sqrt{25 \sqrt{7}}$

Step 4

Rewrite $25$ as $5^{2}$ .

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

Step 5

Pull terms out from under the radical.

$5 \sqrt{\sqrt{7}}$

Step 6

Rewrite $\sqrt{\sqrt{7}}$ as $\sqrt[4]{7}$ .

$5 \sqrt[4]{7}$

Step 7

The result can be shown in multiple forms.

Exact Form:

$5 \sqrt[4]{7}$

Decimal Form:

$8.13288280 \dots$