Question

Simplify :- √81 4 − 8√343 3 + 15√32 5 + √225​

Answer 1

Answer:

Let

E = ⁴√81 - 8(³√216) + 15(⁶√32) + (√225)

We shall only consider positive roots of all the terms of the expression E.

81 = (3)⁴, => ⁴√81 = ⁴√(3)⁴ = 3,

216 = (6)³,=> 8(³√216) = 8[³√(6)³] = 8 × 6 = 48,

32 =(2)⁵, => 15(⁵√32) = 15[⁵√32] = 15 × 2 = 30

225 = (15)², => (√225) = [²√(15)²] = 15.

E = 3 - 48 + 30 + 15 = 48 - 48 = 0.