Pre-Algebra Examples

$2 \sqrt{24} \div \sqrt{32}$

Step 1

Rewrite the division as a fraction.

$\frac{2 \sqrt{24}}{\sqrt{32}}$

Step 2

Combine $\sqrt{24}$ and $\sqrt{32}$ into a single radical.

$2 \sqrt{\frac{24}{32}}$

Step 3

Cancel the common factor of $24$ and $32$ .

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Step 3.1

Factor $8$ out of $24$ .

$2 \sqrt{\frac{8 (3)}{32}}$

Step 3.2

Cancel the common factors.

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Step 3.2.1

Factor $8$ out of $32$ .

$2 \sqrt{\frac{8 \cdot 3}{8 \cdot 4}}$

Step 3.2.2

Cancel the common factor.

$2 \sqrt{\frac{8 \cdot 3}{8 \cdot 4}}$

Step 3.2.3

Rewrite the expression.

$2 \sqrt{\frac{3}{4}}$

Step 4

Rewrite $\sqrt{\frac{3}{4}}$ as $\frac{\sqrt{3}}{\sqrt{4}}$ .

$2 \frac{\sqrt{3}}{\sqrt{4}}$

Step 5

Simplify the denominator.

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Step 5.1

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

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

Step 5.2

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

$2 \frac{\sqrt{3}}{2}$

Step 6

Cancel the common factor of $2$ .

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Step 6.1

Cancel the common factor.

$2 \frac{\sqrt{3}}{2}$

Step 6.2

Rewrite the expression.

$\sqrt{3}$

Step 7

The result can be shown in multiple forms.

Exact Form:

$\sqrt{3}$

Decimal Form:

$1.73205080 \dots$