Question

simplify root6/root2+root3 + 3 root2/root6 + root3

Answer 1

Root6* root6 + root3(root12) + 3root (root2) + root3(root12 ) /root 12

6+6+6+6/2*2root3

24/2root3

12/root3

4root3

Answer 2

Answer:

$\frac{\sqrt6}{\sqrt 2}+\sqrt 3+\frac{3\sqrt2}{\sqrt 6}+\sqrt 3=4\sqrt 3$

Step-by-step explanation:

Given : Expression  $\frac{\sqrt6}{\sqrt 2}+\sqrt 3+\frac{3\sqrt2}{\sqrt 6}+\sqrt 3$

To find : The simplification of the given expression?

Solution :

$\frac{\sqrt6}{\sqrt 2}+\sqrt 3+\frac{3\sqrt2}{\sqrt 6}+\sqrt 3$

$=\frac{\sqrt6}{\sqrt 2}+2\sqrt 3+\frac{3\sqrt2}{\sqrt 6}$

$=\frac{\sqrt 6\times\sqrt6+2\sqrt 3(\sqrt 2\times \sqrt 6)+3\sqrt2\times \sqrt2}{\sqrt 2\times \sqrt 6}$

$=\frac{6+2\times 3\times 2+3\times 2}{2\sqrt 3}$

$=\frac{6+12+6}{2\sqrt 3}$

$=\frac{24}{2\sqrt 3}$

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

$=4\sqrt 3$

Therefore, $\frac{\sqrt6}{\sqrt 2}+\sqrt 3+\frac{3\sqrt2}{\sqrt 6}+\sqrt 3=4\sqrt 3$