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Question
If \[\sqrt{2} = 1 . 4142\] then \[\sqrt{\frac{\sqrt{2} - 1}{\sqrt{2} + 1}}\] is equal to
Options
0.1718
5.8282
0.4142
2.4142
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Solution
0.4142
Explanation:
Given that `sqrt2= 1.4142`, we need to find the value of `sqrt((sqrt2-1)/(sqrt2+1))`
We can rationalize the denominator of the given expression. We know that rationalization factor for `sqrt2+1` is`sqrt2-1`. We will multiply numerator and denominator of the given expression `sqrt((sqrt2-1)/(sqrt2+1))`by`sqrt2-1`, to get
`sqrt((sqrt2-1)/(sqrt2+1)) = sqrt((sqrt2-1)/(sqrt2+1)xxsqrt((sqrt2-1)/(sqrt2-1)))`
` = sqrt((sqrt2-1)^2/((sqrt2)^2-1))`
` = sqrt((sqrt2-1)^2)/(sqrt((sqrt2)^2-1))`
\[\sqrt{\frac{\sqrt{2} - 1}{\sqrt{2} + 1}} = \frac{\sqrt{2} - 1}{1}\]
Putting the value of `sqrt2`, we get
`sqrt2 -1 = 4.4142 - 1`
`= 0.4142`
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