Question

Rationalise the denominator in each of the following and hence evaluate by taking $\sqrt{2}=1.414,\sqrt{3}=1.732$ and $\sqrt{5}=2.236$, upto three places of decimal. :$\frac{\sqrt{10}-\sqrt{5}}{2}$

• A. $0.453$
• B. $0.465$
• C. $0.455$
• D. $0.463$

Answer 1

The correct option is D $0.463$

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

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

$=\frac{\sqrt{5}(\sqrt{2}-1)}{2}$

$=\frac{2.236(1.414-1)}{2}$

$=\frac{2.236\times 0.414}{2}$

$=0.463$