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Question
Simplify the following:
`root(4)(81) - 8root(3)(216) + 15root(5)(32) + sqrt(225)`
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Solution
`root(4)(81) - 8root(3)(216) + 15root(5)(32) + sqrt(225) = (81)^(1/4) - 8 xx (216)^(1/3) + 15 xx (32)^(1/5) + sqrt((15)^2` ...`[∵ root(m)(a) = a^(1/m)]`
= `(3^4)^(1/4) - 8 xx (6^3)^(1/3) + 15 xx (2^5)^(1/5) + 15`
= `3^(4 xx 1/4) - 8 xx 6^(3 xx 1/3) + 15 xx 2^(5 xx 1/5) + 15` ...[∵ (am)n = amn]
= 31 – 8 × 61 + 15 × 21 + 15
= 3 – 48 + 30 + 15
= 48 – 48
= 0
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