Question

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

Answer 1

Question :

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

Answer :

➳ $\bold0$

Explanation :

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

⟹ $\sqrt[4]{3^4} - 8 \sqrt[3]{6^3} + 15 \sqrt[5]{2^5} + \sqrt{15^2}$

⟹ $3\:-\:(\:8\:×\:6\:)\:+\:(\:15\:×\:2\:)\:+\:15$

⟹ $3\:-\:48\:+\:30\:+\:15$

⟹ $48\:-\:48$

⟹ $\bold0$

Steps :

• $\sqrt[4]{81}$ can be written as $\sqrt[4]{3^4}$ $\boxed{3×3×3×3=81}$

• $8 \sqrt[3]{216}$ can be written as $8 \sqrt[3]{6^3}$ $\boxed{6×6×6=216}$

• $15 \sqrt[5]{32}$ can be written as $5 \sqrt[5]{2^5}$ $\boxed{2×2×2×2×2=32}$

• $\sqrt{225}$ can be written as $\sqrt{15^2}$ $\boxed{15×15=225}$

Cancellation :

⟶ ${\cancel{4}}\sqrt3^{\cancel{4}}$ - $8\:{\cancel{3}}\sqrt6^{\cancel{3}}$ + $15\:{\cancel{5}}\sqrt2^{\cancel{5}}$

So, It's Done !!