Question

4√81-8³√216 + 15³ √32 +√225​

Answer 1

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$4 \sqrt{81} - {8} \sqrt[3]{216} + 15 \sqrt[3]{32} + \sqrt{225}$

$4 \times 9 - 8 \sqrt[3]{ {6}^{3} } + 15 \sqrt[3]{ {2}^{3} \times {2}^{2} } + 15$

$36 - 8 \times 6 + 15 \times 2 \sqrt[3]{ {2}^{2} } + 15$

$51- 48 + 30 \sqrt[3]{4}$

$3 + 30 \sqrt[3]{4}$

Answer 2

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.

Hope it helps..!!