Question

Value of :-
$\sqrt{6 + 2 \sqrt{5} + \sqrt{8} + 2 \sqrt{6} }$
​

Answer 1

$\huge{\bold{SOLUTION:-}}$

$\sqrt{6 + 2 \sqrt{3} + \sqrt{8} + 2 \sqrt{6} }$

$\sqrt{6 + 2 \sqrt{3} + 2 \sqrt{2} + 2 \sqrt{6} }$

$\sqrt{3 + 1 + 2 + 2 \sqrt{3 \times 1} + 2 \sqrt{1 \times 2} + 2 \sqrt{3 \times 2} }$

$\sqrt{ {( \sqrt{3} + \sqrt{1} + \sqrt{2} )}^{2} }$

$\sqrt{3} + \sqrt{1} + \sqrt{2}$

$\bold{\underline{\underline{EXPLANATION:-}}}$

An easy trick to solve this problem is just simplifying every term inside the root.

When a irrational number is multiplied with other irrational , the product need not be irrational number.

For example ,

when root 2 and root 8 are multiplied, product is root 16 i.e. 4

Here the product is 4 which is rational number.

The sum of two irrational numbers need not to be irrational

For example,

root 2 +(-root 2 )=0 which is a rational number

By knowing some of the basic properties , we can easily simplify any type of problem.