Question

find the square root of 11+2 root 30

Answer 1

Given that,

An expression, ${11+2\sqrt{30}$

To find,

The square root of the expression.

Solution,

Let x is the given expression. So,

$x=\sqrt{11+2\sqrt{30} }$

We can split 11 as 6 + 5. So,

$x={6+5+2\sqrt{30}$

We can write the above expression as follows :

$x=(\sqrt6)^2+(\sqrt5)^2+2\times \sqrt 6\times \sqrt 5$

We know that, $a^2+b^2+2ab=(a+b)^2$

So,

$x=(\sqrt6+\sqrt5)^2$

Taking root both sides :

$\sqrt{x} =\sqrt{(\sqrt6+\sqrt5)^2} \\\\\sqrt{x}= \sqrt6+\sqrt5$

So, we can say that the square root of the given expression is $\sqrt6+\sqrt5$. Hence, this is the required solution.

Answer 2

Answer:

answer is square root of 5 + 6