Simplify square root of 25/16- square root of 36/25

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

Step 1

Simplify each term.

Rewrite

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

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

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

Simplify the numerator.

Rewrite

$25$ as

$5^{2}$ .

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

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

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

Simplify the denominator.

Rewrite

$16$ as

$4^{2}$ .

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

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

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

Rewrite

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

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

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

Simplify the numerator.

Rewrite

$36$ as

$6^{2}$ .

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

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

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

Simplify the denominator.

Rewrite

$25$ as

$5^{2}$ .

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

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

$1$ .

Multiply

$\frac{5}{4}$ by

$\frac{5}{5}$ .

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

Multiply

$4$ by

$5$ .

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

Multiply

$\frac{6}{5}$ by

$\frac{4}{4}$ .

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

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.

Multiply

$5$ by

$5$ .

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

Multiply

$- 6$ by

$4$ .

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

Subtract

$24$ from

$25$ .

$\frac{1}{20}$

Step 7

The result can be shown in multiple forms.

Exact Form:

$\frac{1}{20}$

Decimal Form:

$0.05$

Simplify square root of 25/16- square root of 36/25

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