Question

Evaluate: 40 upon 2 root 10 + root 20 + root 40 - 2 root 5, when root 10 is 3.162.

Answer 1

$\frac{40}{ 2\sqrt{10} } + \sqrt{20} + \sqrt{40} - 2 \sqrt{5} \\ = \frac{20}{ \sqrt{10} } + 2 \sqrt{5} + 2 \sqrt{10} - 2 \sqrt{5} \\ = \frac{20 \sqrt{10} }{ \sqrt{10} \sqrt{10} } + 2 \sqrt{10} \\ = \frac{20 \sqrt{10} }{10} + 2 \sqrt{10} \\ = 2 \sqrt{10} + 2 \sqrt{10} \\ = 4 \sqrt{10} \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: given \: \sqrt{10} = 3.162 \\ = 4 \times 3.162 \\ = 12.648 \: \: \: ans$