Question

Simplify the following: -3/root3 + root2 -( 3root2/root6 + root3) + (4root3/root6 + root2)

Answer 1

Answer:

√6÷(√2+√3)+3√2÷(√6+√3)-4√3÷(√6+√2)

Step-by-step explanation:

√6. 3√2(√6+√3)

_____________. × ________________

(√2+√3). -4√3(√6+√2)

Answer 2

$\displaystyle\huge\red{\underline{\underline{Solution}}}$

First Part

$\displaystyle \: \frac{3}{( \sqrt{3} + \sqrt{2} \: ) }$

$= \displaystyle \: \frac{3( \sqrt{3} - \sqrt{2} \: )}{( \sqrt{3} + \sqrt{2} \: )( \sqrt{3} - \sqrt{2} \: ) }$

$= \displaystyle \: \frac{3( \sqrt{3} - \sqrt{2} \: )}{ {( \sqrt{3}) }^{2} - {( \sqrt{2} )}^{2} }$

$= \displaystyle \: \frac{3( \sqrt{3} - \sqrt{2} \: )}{3 - 2}$

$= \displaystyle \: (3 \sqrt{3} - 3\sqrt{2} \: )$

Second Part

$= \displaystyle \: - \frac{3 \sqrt{2} \: }{( \sqrt{6} + \sqrt{3} \: ) }$

$= \displaystyle \: - \frac{3 \sqrt{2} \:( \sqrt{6} - \sqrt{3} \: ) }{( \sqrt{6} + \sqrt{3} \: )( \sqrt{6} - \sqrt{3} \: ) }$

$= \displaystyle \: - \frac{3 \sqrt{2} \:( \sqrt{6} - \sqrt{3} \: ) }{6 - 3 }$

$= \displaystyle \: - \sqrt{2} \:( \sqrt{6} - \sqrt{3} \: )$

$= - \sqrt{12} + \sqrt{6}$

Third Part

$= \displaystyle \: \frac{4 \sqrt{3} \: }{( \sqrt{6} + \sqrt{2} \: ) }$

$= \displaystyle \: \frac{4 \sqrt{3} \:( \sqrt{6} - \sqrt{2} \: ) }{( \sqrt{6} + \sqrt{2} \: )( \sqrt{6} - \sqrt{2} \: ) }$

$= \displaystyle \: \frac{4 \sqrt{3} \:( \sqrt{6} - \sqrt{2} \: ) }{(6 - 2) }$

$= \displaystyle \: \frac{4 \sqrt{3} \:( \sqrt{6} - \sqrt{2} \: ) }{( 6 - 2 )}$

$= \displaystyle \: \frac{4 \sqrt{3} \:( \sqrt{6} - \sqrt{2} \: ) }{( 4 )}$

$= \displaystyle \: \:( \sqrt{18} - \sqrt{6} \: )$

So given expression

$= \displaystyle \: (3 \sqrt{3} - 3\sqrt{2} \: ) - \sqrt{12} + \sqrt{6} + \displaystyle \: \:( \sqrt{18} - \sqrt{6} \: )$

$= 3 \sqrt{3} - \sqrt{12}$

$= 3 \sqrt{3} - 2 \sqrt{3}$

$= \sqrt{3}$