Question

Can anyone solve this?

Answer 1

Solution:

$(28 + 10 \sqrt{3} ) \frac{1}{2} - (7 - 4 \sqrt{3} ) \frac{1}{2}$

$= \sqrt{28 + 10 \sqrt{3} } - \sqrt{7 - 4 \sqrt{3} }$

$= \sqrt{(5 + \sqrt{3}) ^{2} } - \sqrt{(2 - \sqrt{3})^{2} }$

$= 5 + \sqrt{3} - (2 - \sqrt{3} )$

$= 5 + \sqrt{3} - 2 + \sqrt{3}$

$= 3 + \sqrt{3} + \sqrt{3}$

$= 3 + 2 \sqrt{3}$

$= 3 + 3.4641$

$= 6.4641$