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Question
Find the value of `6/(sqrt5 - sqrt3)` it being given that `sqrt3 = 1.732` and `sqrt5 = 2.236`
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Solution
We know that rationalization factor for `sqrt5 - sqrt3` is `sqrt5 + sqrt3`. We will multiply denominator and numerator of the given expression `6/(sqrt5 - sqrt3)` by `sqrt5 + sqrt3` to get
`6/(sqrt5 - sqrt3) xx (sqrt5 + sqrt3)/(sqrt5 + sqrt3) = (6sqrt5 + 6sqrt3)/((sqrt5)^2 - (sqrt3)^3)`
`= (6sqrt5 + 6sqrt3)/(5 - 3)`
`= (6sqrt5 + 6sqrt3)/2`
`= 3sqrt5 + 3sqrt3`
Putting the values of `sqrt5` and `sqrt3` we get
`3sqrt5 + 3sqrt3 = 3(2.236) + 3(1.732)`
= 6.708 + 5.196
= 11.904
Hence value of the given expression is 11.904
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