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. :$$\dfrac{\sqrt{10}-\sqrt{5}}{2}$$

A
0.453
B
0.465
C
0.455
D
0.463

Solution

## The correct option is D $$0.463$$$$\dfrac { \sqrt { 10 } -\sqrt { 5 } }{ 2 }$$$$=\dfrac { \sqrt { 2 } \times \sqrt { 5 } -\sqrt { 5 } }{ 2 }$$$$=\dfrac { \sqrt { 5 } \left( \sqrt { 2 } -1 \right) }{ 2 }$$$$=\dfrac { 2.236\left( 1.414-1 \right) }{ 2 }$$$$=\dfrac { 2.236\times 0.414 }{ 2 }$$$$=0.463$$ Mathematics

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