Pre-Algebra Examples

$\frac{8}{\sqrt{75}}$

Step 1

Simplify the denominator.

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Step 1.1

Rewrite $75$ as $5^{2} \cdot 3$ .

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Step 1.1.1

Factor $25$ out of $75$ .

$\frac{8}{\sqrt{25 (3)}}$

Step 1.1.2

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

$\frac{8}{\sqrt{5^{2} \cdot 3}}$

Step 1.2

Pull terms out from under the radical.

$\frac{8}{5 \sqrt{3}}$

Step 2

Multiply $\frac{8}{5 \sqrt{3}}$ by $\frac{\sqrt{3}}{\sqrt{3}}$ .

$\frac{8}{5 \sqrt{3}} \cdot \frac{\sqrt{3}}{\sqrt{3}}$

Step 3

Combine and simplify the denominator.

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Step 3.1

Multiply $\frac{8}{5 \sqrt{3}}$ by $\frac{\sqrt{3}}{\sqrt{3}}$ .

$\frac{8 \sqrt{3}}{5 \sqrt{3} \sqrt{3}}$

Step 3.2

Move $\sqrt{3}$ .

$\frac{8 \sqrt{3}}{5 (\sqrt{3} \sqrt{3})}$

Step 3.3

Raise $\sqrt{3}$ to the power of $1$ .

$\frac{8 \sqrt{3}}{5 ({\sqrt{3}}^{1} \sqrt{3})}$

Step 3.4

Raise $\sqrt{3}$ to the power of $1$ .

$\frac{8 \sqrt{3}}{5 ({\sqrt{3}}^{1} {\sqrt{3}}^{1})}$

Step 3.5

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

$\frac{8 \sqrt{3}}{5 {\sqrt{3}}^{1 + 1}}$

Step 3.6

Add $1$ and $1$ .

$\frac{8 \sqrt{3}}{5 {\sqrt{3}}^{2}}$

Step 3.7

Rewrite ${\sqrt{3}}^{2}$ as $3$ .

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Step 3.7.1

Use $\sqrt[n]{a^{x}} = a^{\frac{x}{n}}$ to rewrite $\sqrt{3}$ as $3^{\frac{1}{2}}$ .

$\frac{8 \sqrt{3}}{5 {(3^{\frac{1}{2}})}^{2}}$

Step 3.7.2

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

$\frac{8 \sqrt{3}}{5 \cdot 3^{\frac{1}{2} \cdot 2}}$

Step 3.7.3

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

$\frac{8 \sqrt{3}}{5 \cdot 3^{\frac{2}{2}}}$

Step 3.7.4

Cancel the common factor of $2$ .

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Step 3.7.4.1

Cancel the common factor.

$\frac{8 \sqrt{3}}{5 \cdot 3^{\frac{2}{2}}}$

Step 3.7.4.2

Rewrite the expression.

$\frac{8 \sqrt{3}}{5 \cdot 3^{1}}$

Step 3.7.5

Evaluate the exponent.

$\frac{8 \sqrt{3}}{5 \cdot 3}$

Step 4

Multiply $5$ by $3$ .

$\frac{8 \sqrt{3}}{15}$

Step 5

The result can be shown in multiple forms.

Exact Form:

$\frac{8 \sqrt{3}}{15}$

Decimal Form:

$0.92376043 \dots$