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Question
Simplify the following expressions:
`(sqrt5 - 2)(sqrt3 - sqrt5)`
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Solution
We can simplify the expression `(sqrt5 - 2)(sqrt3 - sqrt5)` as
`(sqrt5 - 2)(sqrt3 - sqrt5) = sqrt5 xx sqrt3 - sqrt5 xx sqrt5 - 2 xx sqrt3 + 2 xx sqrt5`
`= sqrt15 - sqrt(5 xx 5) - 2sqrt3 + 2sqrt5`
`=sqrt15 - (5^2)^(1/2) - 2sqrt3 +2sqrt5`
`= sqrt15 - (5^2)^(1/2) - 2sqrt3 + 2sqrt5`
`= sqrt15 - 5^1 - 2sqrt3 + 2sqrt5`
Hence the value of the expression is `sqrt15 - 2sqrt3 + 2sqrt5 - 5`
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