Question

find the square root of 7+4root 3

Answer 1

$7 + 4 \sqrt{3} = 7 + 2 \times 2 \sqrt{3} \\ = 4 + 3 + 2 \times 2 \sqrt{3} \\ {2}^{2} + { \sqrt{3} }^{2} + 2 \times 2 \times \sqrt{3} \\ = {(2 + \sqrt{3}) }^{2} \\ therefore \\ \sqrt{7 + 4 \sqrt{3} } = + \: \: or \: \: - (2 + \sqrt{3} )$