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Question
Evaluate, correct to one place of decimal, the expression `5/(sqrt20 - sqrt10)`, if `sqrt5` = 2.2 and `sqrt10` = 3.2.
Solution
Given - `sqrt5` = 2.2 and `sqrt10` = 3.2.
`5/(sqrt20 - sqrt10)`
`= 5/(sqrt20 - sqrt10) xx (sqrt20 + sqrt10)/(sqrt20 + sqrt10)`
`= (5 (sqrt(20) + sqrt10))/(20 - 10)`
`= (cancel(5)^1 (sqrt(20) + sqrt10))/(cancel(10)_2)`
`= (sqrt(20) + sqrt10)/2`
`= (sqrt(4 xx 5) + sqrt10)/2`
`= (2sqrt5 + sqrt10)/2`
`= (2(2.2) + 3.2)/2`
`= (4.4 + 3.2)/2`
`= 7.6/2`
= 3.8
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