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Question
If `sqrt(2) = 1.4142`, then `sqrt((sqrt(2) - 1)/(sqrt(2) + 1))` is equal to ______.
Options
2.4142
5.8282
0.4142
0.1718
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Solution
If `sqrt(2) = 1.4142`, then `sqrt((sqrt(2) - 1)/(sqrt(2) + 1))` is equal to 0.4142.
Explanation:
`sqrt((sqrt(2) - 1)/(sqrt(2) + 1)) = sqrt((sqrt(2) - 1)/(sqrt(2) + 1) xx (sqrt(2) - 1)/(sqrt(2) - 1))`
= `sqrt((sqrt(2) - 1)^2/((sqrt(2))^2 - 1^2)`
= `sqrt((sqrt(2) - 1)^2/(2 - 1)`
= `sqrt((sqrt(2) - 1)^2/1`
= 1.4142 – 1
= 0.4142
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