Question

simplify and rationalise and find the value of:

Answer 1

3. 
we rationalize the denominator by multiplying with √2 in the numerator and denominator.
Given  √5 = 2.236      and    √2 = 1.414

$\frac{\sqrt{10}-\sqrt5}{2\sqrt2}\\\\=\frac{\sqrt2\ (\sqrt{2*5}-\sqrt5)}{\sqrt2\ 2\ \sqrt2}\\\\=\frac{\sqrt2*\sqrt{2}*\sqrt{5}-\sqrt2*\sqrt5}{2\ \sqrt2\ \sqrt2}\\\\=\frac{(2-\sqrt2)\sqrt5}{2*2}\\\\=\frac{(2-1.414)\ *\ 2.236}{4}\\\\=0.327$

We have rationalized in such a way that, we use the values of  √2 and √5 only at one place in the computation.