Question

If √10=3.162 and √5=2.236,find The Value Of (√10-√5)/√2

Answer 1

Given :

$\sqrt{10} = 3.162$

$\sqrt{5} = 2.236$

Solution :

$= \frac{ ( \sqrt{10} - \sqrt{5} )}{ \sqrt{2} } \\ \\ squaring \: \: numerator \: \: and \: \: denominator \\ \\ = \frac{ {( \sqrt{10 } - \sqrt{5})}^{2} }{{ (\sqrt{2}})^{2} } \\ \\ {(x - y)}^{2} = {x}^{2} + {y}^{2} - 2xy \\ \\ = \frac{ { (\sqrt{10} )}^{2} + {(5)}^{2} - 2 \times \sqrt{10} \times \sqrt{5} }{2} \\ \\ = \frac{10 + 25 - 2 \times3.162 \times 2.236 }{2} \\ \\ = \frac{35 - 14.140464}{2} \\ \\ = \frac{20.859536}{2} \\ \\ = 10.429768 \\ \\ = 10.43$

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