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Question
Simplify the following using addition and subtraction properties of surds:
`3sqrt(75) + 5sqrt(48) - sqrt(243)`
Solution
`3sqrt(75) + 5sqrt(48) - sqrt(243)`
= `3sqrt(5^2 xx 3) + 5sqrt(2^4 xx 3) - sqrt(3^5)`
= `3 xx 5sqrt(3) + 5 xx 2^2sqrt(3) - 3^2sqrt(3)`
= `15sqrt(3) + 20sqrt(3) - 9sqrt(3)`
= `(15 + 20 - 9)sqrt(3)`
= `(35 - 9)sqrt(3)`
= `26sqrt(3)`
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