Question

Find the value of y = √10− √5 / √2 to three places of decimals using the values √2 = 1.414 and √10 = 3.162 (approx.)

Answer 1

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

$= \frac{\sqrt{2}(\sqrt{10} - \sqrt{5})}{\sqrt{2}\times \sqrt{2}}$

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

$= \frac{\sqrt{10}( \sqrt{2} - 1)}{2}$

$=\frac{ 3.162( 1.414- 1 )}{2}$

$= \frac{ 3.162 \times 0.414}{2}$

$= 3.162 \times 0.207$

$= 0.654534$

Therefore.,

$\red{ Value \:of \: y } \green { = 0 654534}$

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Answer 2

Given :-

$\sf y = \frac{\sqrt{10} - \sqrt{5} }{ \sqrt{2} }$

To Find :-

• Value of 'y'

Solution :-

$\sf y = \frac{\sqrt{10} - \sqrt{5} }{ \sqrt{2} }$

$\implies\sf\frac{\sqrt{2}(\sqrt{10} - \sqrt{5})}{\sqrt{2}\times \sqrt{2}}</p><p>$

$\implies\sf\frac{ \sqrt{2} \times \sqrt{10} - \sqrt{2}\times \sqrt{5}}{2}$

$\implies\sf\frac{\sqrt{10}( \sqrt{2} - 1)}{2}$

$\implies\sf\frac{ 3.162( 1.414- 1 )}{2}$

$\implies\sf\frac{ 3.162 \times 0.414}{2}$

$\implies\sf3.162 \times 0.207$

$\implies\sf0.654534$

Answer :-

• Value of 'y' is 0.654534