Question

simplify question

please solve it​

Answer 1

ANSWER:

To Simplify:

• √(5+2√6)

Solution:

We are given that,

$\implies\sqrt{5+2\sqrt6}$

We can rewrite it as,

$\implies\sqrt{5+2(\sqrt2)(\sqrt3)}$

$\implies\sqrt{2+3+2(\sqrt2)(\sqrt3)}$

So,

$\implies\sqrt{(\sqrt2)^2+(\sqrt3)^2+2(\sqrt2)(\sqrt3)}$

We know that,

$\hookrightarrow a^2+b^2+2ab=(a+b)^2$

Here, a = √2 and b=√3.

So,

$\implies\sqrt{(\sqrt2)^2+(\sqrt3)^2+2(\sqrt2)(\sqrt3)}$

$\implies\sqrt{(\sqrt2+\sqrt3)^2}$

So, the square root and the square get cancelled. So,

$\implies\sqrt{(\sqrt2+\sqrt3)^2}$

$\implies\pm\sqrt2+\sqrt3$

Therefore,

$\implies\bf\sqrt{5+2\sqrt6}=\pm\sqrt2+\sqrt3$

Answer 2

Answer:

solution is in the picture