Basic Math Examples

$\sqrt{\frac{25}{16}} - \sqrt{\frac{36}{25}}$

Step 1

Simplify each term.

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Step 1.1

Rewrite $\sqrt{\frac{25}{16}}$ as $\frac{\sqrt{25}}{\sqrt{16}}$ .

$\frac{\sqrt{25}}{\sqrt{16}} - \sqrt{\frac{36}{25}}$

Step 1.2

Simplify the numerator.

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Step 1.2.1

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

$\frac{\sqrt{5^{2}}}{\sqrt{16}} - \sqrt{\frac{36}{25}}$

Step 1.2.2

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

$\frac{5}{\sqrt{16}} - \sqrt{\frac{36}{25}}$

Step 1.3

Simplify the denominator.

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Step 1.3.1

Rewrite $16$ as $4^{2}$ .

$\frac{5}{\sqrt{4^{2}}} - \sqrt{\frac{36}{25}}$

Step 1.3.2

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

$\frac{5}{4} - \sqrt{\frac{36}{25}}$

Step 1.4

Rewrite $\sqrt{\frac{36}{25}}$ as $\frac{\sqrt{36}}{\sqrt{25}}$ .

$\frac{5}{4} - \frac{\sqrt{36}}{\sqrt{25}}$

Step 1.5

Simplify the numerator.

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Step 1.5.1

Rewrite $36$ as $6^{2}$ .

$\frac{5}{4} - \frac{\sqrt{6^{2}}}{\sqrt{25}}$

Step 1.5.2

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

$\frac{5}{4} - \frac{6}{\sqrt{25}}$

Step 1.6

Simplify the denominator.

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Step 1.6.1

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

$\frac{5}{4} - \frac{6}{\sqrt{5^{2}}}$

Step 1.6.2

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

$\frac{5}{4} - \frac{6}{5}$

Step 2

To write $\frac{5}{4}$ as a fraction with a common denominator, multiply by $\frac{5}{5}$ .

$\frac{5}{4} \cdot \frac{5}{5} - \frac{6}{5}$

Step 3

To write $- \frac{6}{5}$ as a fraction with a common denominator, multiply by $\frac{4}{4}$ .

$\frac{5}{4} \cdot \frac{5}{5} - \frac{6}{5} \cdot \frac{4}{4}$

Step 4

Write each expression with a common denominator of $20$ , by multiplying each by an appropriate factor of $1$ .

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Step 4.1

Multiply $\frac{5}{4}$ by $\frac{5}{5}$ .

$\frac{5 \cdot 5}{4 \cdot 5} - \frac{6}{5} \cdot \frac{4}{4}$

Step 4.2

Multiply $4$ by $5$ .

$\frac{5 \cdot 5}{20} - \frac{6}{5} \cdot \frac{4}{4}$

Step 4.3

Multiply $\frac{6}{5}$ by $\frac{4}{4}$ .

$\frac{5 \cdot 5}{20} - \frac{6 \cdot 4}{5 \cdot 4}$

Step 4.4

Multiply $5$ by $4$ .

$\frac{5 \cdot 5}{20} - \frac{6 \cdot 4}{20}$

Step 5

Combine the numerators over the common denominator.

$\frac{5 \cdot 5 - 6 \cdot 4}{20}$

Step 6

Simplify the numerator.

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Step 6.1

Multiply $5$ by $5$ .

$\frac{25 - 6 \cdot 4}{20}$

Step 6.2

Multiply $- 6$ by $4$ .

$\frac{25 - 24}{20}$

Step 6.3

Subtract $24$ from $25$ .

$\frac{1}{20}$

Step 7

The result can be shown in multiple forms.

Exact Form:

$\frac{1}{20}$

Decimal Form:

$0.05$