Question

If $\sqrt[3]{34\frac{12}{125}}=x$, then the value x is:

• A. $1\frac{3}{5}$
• B. $1\frac{2}{5}$
• C. $2\frac{2}{5}$
• D. $1\frac{4}{5}$

Answer 1

The correct option is A

$1\frac{3}{5}$

$\sqrt[3]{34\frac{12}{125}}=\sqrt[3]{3\frac{512}{125}}=\frac{\sqrt[3]{3512}}{\sqrt[3]{3125}}$

Factorizing 512 we get
$\begin{array}{cc}2& 512\\ 2& 256\\ 2& 128\\ 2& 64\\ 2& 32\\ 2& 16\\ 2& 8\\ 2& 4\\ & 2\end{array}$

$\Rightarrow 512=2^3\times 2^3\times 2^3$

$\Rightarrow \sqrt[3]{3512}=2\times 2\times 2=8$

Factorizing 125 we get
$\begin{array}{cc}5& 125\\ 5& 25\\ & 5\end{array}$

$\Rightarrow 125=5^3$

$\Rightarrow \sqrt[3]{3125}=5$

$\therefore \frac{\sqrt[3]{3512}}{\sqrt[3]{3125}}=\frac{8}{5}=1\frac{3}{5}$