Question

find the square root of 11 + 2 root 30

Answer 1

Answer:

$\sqrt{11+2\sqrt{30}}=\sqrt6+\sqrt5$

Step-by-step explanation:

Given : Expression $11+2\sqrt{30}$

To find : The square root of the expression ?

Solution :

Let the expression be,

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

Now, we try to make square by splitting expression

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

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

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

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

Taking root both side,

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

$\sqrt{x}=\sqrt6+\sqrt5$

Therefore, Square root is given by,  $\sqrt{11+2\sqrt{30}}=\sqrt6+\sqrt5$

Answer 2

Answer:

sq11+2 sq 30

sq 5+6+2 sq 5×6

sq (sq5)²+ (sq6)²+2 sq5× sq6

(sq5+ sq6)

sq5+sq6.