Finite Math Examples

$\sqrt{96} \div \sqrt{150} \div \sqrt{32}$

Step 1

Rewrite the division as a fraction.

$\frac{\sqrt{96} \div \sqrt{150}}{\sqrt{32}}$

Step 2

Multiply the numerator by the reciprocal of the denominator.

$\sqrt{96} \div \sqrt{150} \cdot \frac{1}{\sqrt{32}}$

Step 3

Rewrite the division as a fraction.

$\frac{\sqrt{96}}{\sqrt{150}} \cdot \frac{1}{\sqrt{32}}$

Step 4

Combine $\sqrt{96}$ and $\sqrt{150}$ into a single radical.

$\sqrt{\frac{96}{150}} \frac{1}{\sqrt{32}}$

Step 5

Cancel the common factor of $96$ and $150$ .

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Step 5.1

Factor $6$ out of $96$ .

$\sqrt{\frac{6 (16)}{150}} \frac{1}{\sqrt{32}}$

Step 5.2

Cancel the common factors.

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Step 5.2.1

Factor $6$ out of $150$ .

$\sqrt{\frac{6 \cdot 16}{6 \cdot 25}} \frac{1}{\sqrt{32}}$

Step 5.2.2

Cancel the common factor.

$\sqrt{\frac{6 \cdot 16}{6 \cdot 25}} \frac{1}{\sqrt{32}}$

Step 5.2.3

Rewrite the expression.

$\sqrt{\frac{16}{25}} \frac{1}{\sqrt{32}}$

Step 6

Rewrite $\sqrt{\frac{16}{25}}$ as $\frac{\sqrt{16}}{\sqrt{25}}$ .

$\frac{\sqrt{16}}{\sqrt{25}} \cdot \frac{1}{\sqrt{32}}$

Step 7

Simplify the numerator.

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Step 7.1

Rewrite $16$ as $4^{2}$ .

$\frac{\sqrt{4^{2}}}{\sqrt{25}} \cdot \frac{1}{\sqrt{32}}$

Step 7.2

Pull terms out from under the radical, assuming positive real numbers.

$\frac{4}{\sqrt{25}} \cdot \frac{1}{\sqrt{32}}$

Step 8

Simplify the denominator.

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Step 8.1

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

$\frac{4}{\sqrt{5^{2}}} \cdot \frac{1}{\sqrt{32}}$

Step 8.2

Pull terms out from under the radical, assuming positive real numbers.

$\frac{4}{5} \cdot \frac{1}{\sqrt{32}}$

Step 9

Simplify the denominator.

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Step 9.1

Rewrite $32$ as $4^{2} \cdot 2$ .

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Step 9.1.1

Factor $16$ out of $32$ .

$\frac{4}{5} \cdot \frac{1}{\sqrt{16 (2)}}$

Step 9.1.2

Rewrite $16$ as $4^{2}$ .

$\frac{4}{5} \cdot \frac{1}{\sqrt{4^{2} \cdot 2}}$

Step 9.2

Pull terms out from under the radical.

$\frac{4}{5} \cdot \frac{1}{4 \sqrt{2}}$

Step 10

Simplify terms.

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Step 10.1

Cancel the common factor of $4$ .

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Step 10.1.1

Factor $4$ out of $4 \sqrt{2}$ .

$\frac{4}{5} \cdot \frac{1}{4 (\sqrt{2})}$

Step 10.1.2

Cancel the common factor.

$\frac{4}{5} \cdot \frac{1}{4 \sqrt{2}}$

Step 10.1.3

Rewrite the expression.

$\frac{1}{5} \cdot \frac{1}{\sqrt{2}}$

Step 10.2

Multiply $\frac{1}{5}$ by $\frac{1}{\sqrt{2}}$ .

$\frac{1}{5 \sqrt{2}}$

Step 11

Multiply $\frac{1}{5 \sqrt{2}}$ by $\frac{\sqrt{2}}{\sqrt{2}}$ .

$\frac{1}{5 \sqrt{2}} \cdot \frac{\sqrt{2}}{\sqrt{2}}$

Step 12

Combine and simplify the denominator.

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Step 12.1

Multiply $\frac{1}{5 \sqrt{2}}$ by $\frac{\sqrt{2}}{\sqrt{2}}$ .

$\frac{\sqrt{2}}{5 \sqrt{2} \sqrt{2}}$

Step 12.2

Move $\sqrt{2}$ .

$\frac{\sqrt{2}}{5 (\sqrt{2} \sqrt{2})}$

Step 12.3

Raise $\sqrt{2}$ to the power of $1$ .

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

Step 12.4

Raise $\sqrt{2}$ to the power of $1$ .

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

Step 12.5

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

$\frac{\sqrt{2}}{5 {\sqrt{2}}^{1 + 1}}$

Step 12.6

Add $1$ and $1$ .

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

Step 12.7

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

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Step 12.7.1

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

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

Step 12.7.2

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

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

Step 12.7.3

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

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

Step 12.7.4

Cancel the common factor of $2$ .

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Step 12.7.4.1

Cancel the common factor.

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

Step 12.7.4.2

Rewrite the expression.

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

Step 12.7.5

Evaluate the exponent.

$\frac{\sqrt{2}}{5 \cdot 2}$

Step 13

Multiply $5$ by $2$ .

$\frac{\sqrt{2}}{10}$

Step 14

The result can be shown in multiple forms.

Exact Form:

$\frac{\sqrt{2}}{10}$

Decimal Form:

$0.14142135 \dots$