Basic Math Examples

\sqrt{\frac{21}{75}}

$\sqrt{\frac{21}{75}}$

Step 1

Cancel the common factor of

21

$21$ and

75

$75$ .

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Step 1.1

Factor

3

$3$ out of

21

$21$ .

\sqrt{\frac{3 (7)}{75}}

$\sqrt{\frac{3 (7)}{75}}$

Step 1.2

Cancel the common factors.

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Step 1.2.1

Factor

3

$3$ out of

75

$75$ .

\sqrt{\frac{3 \cdot 7}{3 \cdot 25}}

$\sqrt{\frac{3 \cdot 7}{3 \cdot 25}}$

Step 1.2.2

Cancel the common factor.

$\sqrt{\frac{3 \cdot 7}{3 \cdot 25}}$

Step 1.2.3

Rewrite the expression.

$\sqrt{\frac{7}{25}}$

Step 2

Rewrite

$\sqrt{\frac{7}{25}}$ as

$\frac{\sqrt{7}}{\sqrt{25}}$ .

$\frac{\sqrt{7}}{\sqrt{25}}$

Step 3

Simplify the denominator.

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Step 3.1

Rewrite

$25$ as

$5^{2}$ .

$\frac{\sqrt{7}}{\sqrt{5^{2}}}$

Step 3.2

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

$\frac{\sqrt{7}}{5}$

Step 4

The result can be shown in multiple forms.

Exact Form:

$\frac{\sqrt{7}}{5}$

Decimal Form:

$0.52915026 \dots$