Algebra Examples

$5 \sqrt{\frac{49 m - 49 n}{25}}$

Step 1

Factor $49$ out of $49 m - 49 n$ .

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Step 1.1

Factor $49$ out of $49 m$ .

$5 \sqrt{\frac{49 (m) - 49 n}{25}}$

Step 1.2

Factor $49$ out of $- 49 n$ .

$5 \sqrt{\frac{49 (m) + 49 (- n)}{25}}$

Step 1.3

Factor $49$ out of $49 (m) + 49 (- n)$ .

$5 \sqrt{\frac{49 (m - n)}{25}}$

Step 2

Rewrite $\frac{49 (m - n)}{25}$ as ${(\frac{7}{5})}^{2} (m - n)$ .

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Step 2.1

Factor the perfect power $7^{2}$ out of $49 (m - n)$ .

$5 \sqrt{\frac{7^{2} (m - n)}{25}}$

Step 2.2

Factor the perfect power $5^{2}$ out of $25$ .

$5 \sqrt{\frac{7^{2} (m - n)}{5^{2} \cdot 1}}$

Step 2.3

Rearrange the fraction $\frac{7^{2} (m - n)}{5^{2} \cdot 1}$ .

$5 \sqrt{{(\frac{7}{5})}^{2} (m - n)}$

Step 3

Pull terms out from under the radical.

$5 (\frac{7}{5} \sqrt{m - n})$

Step 4

Combine $\frac{7}{5}$ and $\sqrt{m - n}$ .

$5 \frac{7 \sqrt{m - n}}{5}$

Step 5

Cancel the common factor of $5$ .

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Step 5.1

Cancel the common factor.

$5 \frac{7 \sqrt{m - n}}{5}$

Step 5.2

Rewrite the expression.

$7 \sqrt{m - n}$