Question

Evaluate : 4/(2√10+ √20+√40-2√5-√80) when it is given that √5= 2.236 , √10= 3.162

Answer 1

$\frac{4}{2 \sqrt{10}+\sqrt{20}+\sqrt{40}-2\sqrt{5}-\sqrt{80} }$

= $\frac{4}{2 \sqrt{10}+2\sqrt{5}+2\sqrt{10}-2\sqrt{5}-4\sqrt{5} }$

= $\frac{2}{ \sqrt{10}+\sqrt{5}+\sqrt{10}-\sqrt{5}-2\sqrt{5} }$

= $\frac{2}{ 2\sqrt{10}-\sqrt{5}-2\sqrt{5} }$

This is the answer. You may put the values if you want to simplify further.