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  • If sqroot = 1.4142 then sqroot2-1 by sqroot 2+1 is equal to : (A)2.4142 (B) 5.8282 (C) 0.4142 (D) 0.1718

If \sqrt{2}= 1\cdot 4142 = 1.4142 then \sqrt{\frac{\sqrt{2}-1}{\sqrt{2}+1}}  is equal to :

(A)2.4142
(B)5.8282
(C)0.4142
(D)0.1718

Answers (1)

Answer.        [C]
Solution
  We have, \sqrt{\frac{\sqrt{2}-1}{\sqrt{2}+1}}
  We have to rationalize it
\sqrt{\frac{\sqrt{2}-1}{\sqrt{2}+1}\times \frac{\sqrt{2}-1}{\sqrt{2}-1}}           [Multiplying numerator and denominator by \sqrt{2}-1]

= \frac{\sqrt{\left ( \sqrt{2}-1 \right )\times\left ( \sqrt{2} -1\right ) }}{\sqrt{\left ( \sqrt{2} \right )^{2}-\left ( 1 \right )^{2}}}      [\because (a – b) (a + b) = a2 – b2]

= \frac{\sqrt{\left ( \sqrt{2}-1 \right )^{2}}}{1}

\sqrt{\left ( \sqrt{2}-1 \right )^{2}}
=\sqrt{2}-1
=1\cdot 4142-1
=0.4142

Hence option C is correct.

 

Posted by

infoexpert27

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