Question

Simplify: 7√3/√10+√3-2√5/√6+√5-3√2/√15+3√2

Answer 1

Hope this helps you friend.

Answer 2

Answer:

Rationalize the denominators

[Rationalization is the process of writing the denomination of the given fraction again in the numerator and denominator by changing the signs of the given denominator]

$=\left[\frac{7 \sqrt{3}}{\sqrt{10}+\sqrt{3}} \times \frac{\sqrt{10}-\sqrt{3}}{\sqrt{10}-\sqrt{3}}\right]-\left[\frac{2 \sqrt{5}}{\sqrt{6}+\sqrt{5}} \times \frac{\sqrt{6}-\sqrt{5}}{\sqrt{6}-\sqrt{5}}\right]-\left[\frac{3 \sqrt{2}}{\sqrt{15}+3 \sqrt{2}} \times \frac{\sqrt{15}-3 \sqrt{2}}{\sqrt{15}-3 \sqrt{2}}\right]$

In the above done step we have written the rationalized the denominators

$=\left[\frac{7 \sqrt{30}-21}{10-3}\right]-\left[\frac{2 \sqrt{30}-10}{6-5}\right]-\left[\frac{3 \sqrt{30}-18}{15-18}\right]$

Here simple simplifications are done

$=\left[\frac{7 \sqrt{30}-21}{7}\right]-\left[\frac{2 \sqrt{30}-10}{1}\right]-\left[\frac{3 \sqrt{30}-18}{-3}\right]$

In the above step cancellation of the common terms are done

$=\quad[\sqrt{30}-3]-[2 \sqrt{30}-10]-[-\sqrt{30}+6]$

=√30-3 – 2√30-10 +√30  -6  

= 1