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Question
Simplify the following using addition and subtraction properties of surds:
`5root(3)(40) + 2root(3)(625) - 3root(3)(320)`
Solution
`5root(3)(40) + 2root(3)(625) - 3root(3)(320)`
= `5root(3)(2^3 xx 5) + 2root(3)(5^3 xx 5) - 3root(3)(2^3 xx 2^3 xx 5)`
= `5 xx 2root(3)(5) + 2 xx 5root(3)(5) - 3 xx 2 xx 2root(3)(5)`
= `10root(3)(5) + 10root(3)(5) - 12root(3)(5)`
= `20root(3)(5) - 12root(3)(5)`
= `8root(3)(5)`
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