Basic Math Examples

$\sqrt{\frac{45}{125}}$

Step 1

Cancel the common factor of

$45$ and

$125$ .

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Step 1.1

Factor

$5$ out of

$45$ .

$\sqrt{\frac{5 (9)}{125}}$

Step 1.2

Cancel the common factors.

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Step 1.2.1

Factor

$5$ out of

$125$ .

$\sqrt{\frac{5 \cdot 9}{5 \cdot 25}}$

Step 1.2.2

Cancel the common factor.

$\sqrt{\frac{5 \cdot 9}{5 \cdot 25}}$

Step 1.2.3

Rewrite the expression.

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

Step 2

Rewrite

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

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

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

Step 3

Simplify the numerator.

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Step 3.1

Rewrite

$9$ as

$3^{2}$ .

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

Step 3.2

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

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

Step 4

Simplify the denominator.

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Step 4.1

Rewrite

$25$ as

$5^{2}$ .

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

Step 4.2

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

$\frac{3}{5}$

Step 5

The result can be shown in multiple forms.

Exact Form:

$\frac{3}{5}$

Decimal Form:

$0.6$

$\sqrt[]{\frac{45}{125}}$

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