Question

find the square root of 11+2 root30​

Answer 1

Step-by-step explanation:

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} }x=

11+2

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 5x=(

6

)

2

+(

5

)

2

+2×

6

×

5

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

2

+b

2

+2ab=(a+b)

2

So,

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

6

+

5

)

2

Taking root both sides :

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

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