Question

The positive square root of \[7 + \sqrt{48}\] is 

Options

• \[7 + 2\sqrt{3}\]

• \[7 + \sqrt{3}\]

• \[ \sqrt{3}+2\]

• \[3 + \sqrt{2}\]

Answer 1

Given that:`7 +sqrt48`.To find square root of the given expression we need to rewrite the expression in the form  `a^2 +b^2 +2ab = (a+b)^2`

`7 +sqrt48  = 3+4+2xx2xxsqrt3`

` = (sqrt3)^2 + (2)^2 +2 xx 2xx xxsqrt3`

`= (sqrt3 + 2 )^2`

Hence the square root of the given expression is `sqrt3+2`