Algebra Examples

$\sqrt{\frac{20}{9}}$

Step 1

Rewrite $\sqrt{\frac{20}{9}}$ as $\frac{\sqrt{20}}{\sqrt{9}}$ .

$\frac{\sqrt{20}}{\sqrt{9}}$

Step 2

Simplify the numerator.

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Step 2.1

Rewrite $20$ as $2^{2} \cdot 5$ .

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Step 2.1.1

Factor $4$ out of $20$ .

$\frac{\sqrt{4 (5)}}{\sqrt{9}}$

Step 2.1.2

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

$\frac{\sqrt{2^{2} \cdot 5}}{\sqrt{9}}$

Step 2.2

Pull terms out from under the radical.

$\frac{2 \sqrt{5}}{\sqrt{9}}$

Step 3

Simplify the denominator.

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Step 3.1

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

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

Step 3.2

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

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

Step 4

The result can be shown in multiple forms.

Exact Form:

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

Decimal Form:

$1.49071198 \dots$