Question

Simplify:

$\sqrt[4]{481}-8\sqrt[3]{3216}+15\sqrt[5]{532}+\sqrt{225}$

• A. $0$
• B. $1$
• C. $2$
• D. none of the above

Answer 1

Correct option is A. $0$.

$\sqrt[4]{481}-8\sqrt[3]{3216}+15\sqrt[5]{532}+\sqrt{225}$

$\begin{array}{cc}3& 81\\ 3& 27\\ 3& 9\\ 3& 3\\ & 1\end{array}$

$\Rightarrow \sqrt[4]{481}=\sqrt[4]{43\times 3\times 3\times 3}=3$---(1)

$\begin{array}{cc}2& 216\\ 2& 108\\ 2& 54\\ 2& 27\\ 3& 9\\ 3& 3\\ & 1\end{array}$

$\Rightarrow \sqrt[3]{3216}=\sqrt[3]{3(2\times 3)\times (2\times 3)\times (2\times 3)}=(2\times 3)=6$---(2)

$\begin{array}{cc}2& 32\\ 2& 16\\ 2& 8\\ 2& 4\\ 2& 2\\ & 1\end{array}$

$\Rightarrow \sqrt[5]{532}=\sqrt[5]{52\times 2\times 2\times 2\times 2}=2$ ---(3)

$\begin{array}{cc}3& 225\\ 3& 75\\ 5& 25\\ 5& 5\\ & 1\end{array}$

$\Rightarrow \sqrt{225}=\sqrt{(3\times 5)\times (3\times 5)}=(3\times 5)=15$ ---(4)

Now,

$\sqrt[4]{481}-8\sqrt[3]{3216}+15\sqrt[5]{532}+\sqrt{225}$
$=3-8\left(6\right)+15\left(2\right)+\left(15\right)$

$=3-48+30+15$

$=0$

$\therefore \sqrt[4]{481}-8\sqrt[3]{3216}+15\sqrt[5]{532}+\sqrt{225}=0$