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Question
Given `sqrt(2)` = 1.414, find the value of `(8 - 5sqrt(2))/(3 - 2sqrt(2))` (to 3 places of decimals).
Solution
`(8 - 5sqrt(2))/(3 - 2sqrt(2)) = ((8 - 5sqrt(2))(3 + 2sqrt(2)))/((3 - 2sqrt(2))(3 + 2sqrt(2))`
= `(24 + 16sqrt(2) - 15sqrt(2) - 10 xx 2)/(3^2 - (2sqrt(2))^2`
= `(24 + sqrt(2) - 20)/(9 - 8)`
= `4 + sqrt(2)`
= 4 + 1.414
= 5.414
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