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Question
Simplify the following expressions:
`(sqrt5 - sqrt3)^2`
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Solution
We know that `(a - b)^2 = a^2 + b^2 - 2ab`. We will use this property to simplify the expression
`(sqrt5 - sqrt3)`
`∴ (sqrt5 - sqrt3)^2 = (sqrt5)^2 + (sqrt3)^2 - 2 xx sqrt5 xx sqrt3`
`= sqrt5 xx sqrt5 + sqrt3 xx sqrt3 - 2 xx sqrt(5 xx 3)`
`= sqrt(5 xx 5) + sqrt(3 xx 3) - 2 xx sqrt(5 xx 3)`
`= (5^2)^(1/2) + (3^2)^(1/2) - 2sqrt15`
`= 5^1 + 3^1 - 2sqrt15`
`= 8 - 2sqrt15`
Hence the value of expression is `8 - 2sqrt15`
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