Question

Simplify. 3725−−√−2825−−√+6325−−√ 457√ 7√ 257√ 857√

Answer 1

Answer:

Option A.

Step-by-step explanation:

Consider the given problem is

$3\sqrt{\frac{7}{25}}-\sqrt{\frac{28}{25}}+\sqrt{\frac{63}{25}}$

Using the properties of radical expressions we get

$3\cdot \frac{\sqrt{7}}{\sqrt{25}}-\frac{\sqrt{28}}{\sqrt{25}}+\frac{\sqrt{63}}{\sqrt{25}}$             $[\because \sqrt{\frac{a}{b}}=\frac{\sqrt{a}}{\sqrt{b}}]$

$3\cdot \frac{\sqrt{7}}{\sqrt{25}}-\frac{\sqrt{4}\sqrt{7}}{\sqrt{25}}+\frac{\sqrt{9}\sqrt{7}}{\sqrt{25}}$              $[\because \sqrt{ab}=\sqrt{a}\sqrt{b}]$

$3\cdot \frac{\sqrt{7}}{5}-\frac{2\sqrt{7}}{5}+\frac{3\sqrt{7}}{5}$

Taking out common factors.

$\frac{\sqrt{7}}{5}(3-2+3)$

$\frac{\sqrt{7}}{5}(4)$

$\frac{4\sqrt{7}}{5}$

The simplified form of given expression is $\frac{4}{5}\sqrt{7}$

Therefore, the correct option is A.