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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
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B
0.465
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C
0.455
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D
0.463
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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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