Question

Simplify the following expression
√81 4
-8√216 3
+15√32 5
+√225

Answer 1

$\underline{\textsf{To simplify:}}$

$\mathsf{\sqrt[4]{81}-8\sqrt[3]{216}+15\sqrt[5]{32}+\sqrt{225}}$

$\underline{\textsf{Solution:}}$

$\textsf{Consider,}$

$\mathsf{\sqrt[4]{81}-8\sqrt[3]{216}+15\sqrt[5]{32}+\sqrt{225}}$

$\mathsf{=(81)^\frac{1}{4}-8(216)^\frac{1}{3}+15(32)^\frac{1}{5}+15}$

$\mathsf{=(3^4)^\frac{1}{4}-8(6^3)^\frac{1}{3}+15(2^5)^\frac{1}{5}+15}$

$\mathsf{=3-8(6)+15(2)+15}$

$\mathsf{=3-48+30+15}$

$\mathsf{=0}$

$\underline{\textsf{Answer:}}$

$\mathsf{\sqrt[4]{81}-8\sqrt[3]{216}+15\sqrt[5]{32}+\sqrt{225}=0}$

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