Question

Evaluate under root 5 + 2 under root 6 + under root 8 minus 2 under root 15

Answer 1

$\sqrt{5} + 2 \sqrt{6} + \sqrt{8} - 2 \sqrt{15} \\ \sqrt{5} + 2 \sqrt{6} + 2 \sqrt{2} - 2 \sqrt{3 \times 5} \\ = \sqrt{5} + 2 \sqrt{3} \sqrt{2} + 2 \sqrt{2} - 2 \sqrt{3} \sqrt{5 } \\ = \sqrt{5} (1 - 2 \sqrt{3} ) + 2 \sqrt{2} (1 + \sqrt{3} )$
now put the value of
$\sqrt{2} = 1.414 \\ \sqrt{3} = 1.732 \\ \sqrt{5} = 2.236$
$2.232(1 - 2 \times 1.732) + 2 \times 1.414(1 + 1.732) \\ = 2.232(1 - 3.464) + 2.828(2.732) \\ = 2.232 \times( - 2.464) + 7.726 \\ = - 5.499 + 7.726 \\ = 2.226 \: \: \: \: \: ans$