Question

What is the fully simplified answer to sqrt(7/18) + sqrt(5/8) - sqrt(7/2)

Answer 1

Answer:

$=\frac{-4\sqrt{7}+3\sqrt{5}}{6\sqrt{2}}$

Step-by-step explanation:

Given expression as:

$=\sqrt{\frac{7}{18}}+\sqrt{\frac{5}{8}}-\sqrt{\frac{7}{2} }$

We need to simplify the given expression.

Solution:

We have:

$=\sqrt{\frac{7}{18}}+\sqrt{\frac{5}{8}}-\sqrt{\frac{7}{2} }$

Rewrite the expression as:

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

$\frac{\sqrt{7}}{\sqrt{2} }$ is a common factor to the first two terms.

Using distributive property we can factor out $\frac{\sqrt{7}}{\sqrt{2} }$ from the first two terms.

$=\frac{\sqrt{7}}{\sqrt{2}}(\frac{1}{3} -1) +\frac{\sqrt{5}}{2\sqrt{2}}$

$=\frac{\sqrt{7}}{\sqrt{2}}(\frac{1-3}{3}) +\frac{\sqrt{5}}{2\sqrt{2}}$

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

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

$\sqrt{2}$ is common factor, so we can factor $\sqrt{2}$ from the above expression.

$=\frac{1}{\sqrt{2} }( -\frac{2\sqrt{7}}{3} +\frac{\sqrt{5}}{2})$

$=\frac{1}{\sqrt{2} }( \frac{-2\times 2\sqrt{7}+3\times \sqrt{5}}{6})$

$=\frac{1}{\sqrt{2} }( \frac{-4\sqrt{7}+3\sqrt{5}}{6})$

$=\frac{-4\sqrt{7}+3\sqrt{5}}{6\sqrt{2}}$

Therefore, we get simplified answer as.

$=\frac{-4\sqrt{7}+3\sqrt{5}}{6\sqrt{2}}$