Algebra Examples

$\frac{6 \sqrt{20}}{\sqrt{18}}$

Step 1

Combine $\sqrt{20}$ and $\sqrt{18}$ into a single radical.

$6 \sqrt{\frac{20}{18}}$

Step 2

Cancel the common factor of $20$ and $18$ .

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Step 2.1

Factor $2$ out of $20$ .

$6 \sqrt{\frac{2 (10)}{18}}$

Step 2.2

Cancel the common factors.

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Step 2.2.1

Factor $2$ out of $18$ .

$6 \sqrt{\frac{2 \cdot 10}{2 \cdot 9}}$

Step 2.2.2

Cancel the common factor.

$6 \sqrt{\frac{2 \cdot 10}{2 \cdot 9}}$

Step 2.2.3

Rewrite the expression.

$6 \sqrt{\frac{10}{9}}$

Step 3

Rewrite $\sqrt{\frac{10}{9}}$ as $\frac{\sqrt{10}}{\sqrt{9}}$ .

$6 \frac{\sqrt{10}}{\sqrt{9}}$

Step 4

Simplify the denominator.

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Step 4.1

Rewrite $9$ as $3^{2}$ .

$6 \frac{\sqrt{10}}{\sqrt{3^{2}}}$

Step 4.2

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

$6 \frac{\sqrt{10}}{3}$

Step 5

Cancel the common factor of $3$ .

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Step 5.1

Factor $3$ out of $6$ .

$3 (2) \frac{\sqrt{10}}{3}$

Step 5.2

Cancel the common factor.

$3 \cdot 2 \frac{\sqrt{10}}{3}$

Step 5.3

Rewrite the expression.

$2 \sqrt{10}$

Step 6

The result can be shown in multiple forms.

Exact Form:

$2 \sqrt{10}$

Decimal Form:

$6.32455532 \dots$