Precalculus Examples

$\sqrt{\frac{\frac{18}{25}}{2}}$

Step 1

Multiply the numerator by the reciprocal of the denominator.

$\sqrt{\frac{18}{25} \cdot \frac{1}{2}}$

Step 2

Cancel the common factor of $2$ .

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Step 2.1

Factor $2$ out of $18$ .

$\sqrt{\frac{2 (9)}{25} \cdot \frac{1}{2}}$

Step 2.2

Cancel the common factor.

$\sqrt{\frac{2 \cdot 9}{25} \cdot \frac{1}{2}}$

Step 2.3

Rewrite the expression.

$\sqrt{\frac{9}{25}}$

Step 3

Rewrite $\sqrt{\frac{9}{25}}$ as $\frac{\sqrt{9}}{\sqrt{25}}$ .

$\frac{\sqrt{9}}{\sqrt{25}}$

Step 4

Simplify the numerator.

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Step 4.1

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

$\frac{\sqrt{3^{2}}}{\sqrt{25}}$

Step 4.2

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

$\frac{3}{\sqrt{25}}$

Step 5

Simplify the denominator.

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Step 5.1

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

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

Step 5.2

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

$\frac{3}{5}$

Step 6

The result can be shown in multiple forms.

Exact Form:

$\frac{3}{5}$

Decimal Form:

$0.6$