Question

if √2=1.414 and√5=2.236 find the value √10-√5/2√2 up to three places of decimal

Answer 1

$\sqrt2\approx1.414;\ \sqrt5\approx2.236\\\\\sqrt{10}-\frac{\sqrt5}{2\sqrt2}=\sqrt{2\cdot5}-\frac{\sqrt5}{2\sqrt2}=\sqrt2\cdot\sqrt5-\frac{\sqrt5}{2\sqrt2}\\\\\approx1.414\cdot2.236-\frac{2.236}{2\cdot1.414}=2.551276-\frac{2.236}{2.828}\\\\\approx2.551276-0.7906647=1.7606113\approx1.761$

Answer 2

√10-√15/2√2=√10-√15/2√2*√2/√2=√20-√30/4=2√5-√30/4=√5-√30/4