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Question
Find the values the following correct to three places of decimals, it being given that `sqrt2 = 1.4142`, `sqrt3 = 1.732`, `sqrt5 = 2.2360`, `sqrt6 = 2.4495` and `sqrt10 = 3.162`
`(1 + sqrt2)/(3 - 2sqrt2)`
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Solution
We know that rationalization factor for `3 - 2sqrt2` is `3 + 2sqrt2`. We will multiply numerator and denominator of the given expression `(1 + sqrt2)/(3 - 2sqrt2)` by `3 + 2sqrt2` to get
`(1 + sqrt2)/(3 - 2sqrt2) xx (3 + 2sqrt2)/(3 + 2sqrt2) = (3 + 2 xx sqrt2 + 3 xx sqrt2 + 2 xx (sqrt2)^2)/((3)^2 - (2sqrt2)^2)`
`= (3 + 2sqrt2 + 3sqrt2 + 4)/(9 - 8)`
`= (7 + 5sqrt2)/1`
Putting te value of `sqrt2` we get
`7 + 5sqrt2 = 7 + 5(1.4142)`
= 7 + 7.071
= 14.071
Hence the given expression is simplified to 14.071
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