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Question
The positive square root of \[7 + \sqrt{48}\] is
Options
\[7 + 2\sqrt{3}\]
\[7 + \sqrt{3}\]
\[ \sqrt{3}+2\]
\[3 + \sqrt{2}\]
Solution
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`
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