Question

If 343,000 is a perfect cube, which of the following is its cube root?

• A. 70
• B. 170
• C. 700
• D. 343

Answer 1

The correct option is A 70

To find the cube root of 343000
We know that, $343000=343\times 1000$.

Prime factorise 343:
$\begin{array}{cc}7& 343\\ 7& 49\\ 7& 7\\ & 1\end{array}$
$343=7\times 7\times 7$
So, $\sqrt[3]{3343}=7$

Prime factorise 1000:
$\begin{array}{cc}2& 1000\\ 2& 500\\ 2& 250\\ 5& 125\\ 5& 25\\ 5& 5\\ & 1\end{array}$
$1000=2\times 2\times 2\times 5\times 5\times 5$
So, $\sqrt[3]{31000}=2\times 5=10$

$\Rightarrow \sqrt[3]{3343000}=\sqrt[3]{3343}\times \sqrt[3]{31000}=7\times 10=70$

So, $\sqrt[3]{3343000}=70$