Question

Find the Cube Root of $1000000$.

Answer 1

Hint: Here we have to find the cube root of the given number. Firstly we will find the factor of the number given by using the division method and then we will make a pair of three similar numbers. Finally we will find the cube root of the factors such that we get an integer value outside and hence get our desired answer.

Complete step by step answer:
We have to find the cube root of,
$1000000$
Using Division method we get the factor of above number as,
$\begin{align}
  & 10\left| \!{\underline {\,
  1000000 \,}} \right. \\
 & 10\left| \!{\underline {\,
  100000 \,}} \right. \\
 & 10\left| \!{\underline {\,
  10000 \,}} \right. \\
 & 10\left| \!{\underline {\,
  1000 \,}} \right. \\
 & 10\left| \!{\underline {\,
  100 \,}} \right. \\
 & 10\left| \!{\underline {\,
  10 \,}} \right. \\
 & \,\,\,\,\,\left| \!{\underline {\,
  1 \,}} \right. \\
\end{align}$

So we get the factors as,
$1000000=10\times 10\times 10\times 10\times 10\times 10$
Now as we have to find the cube root we will make the pair of three numbers in above factors,
$1000000=\left( 10\times 10\times 10 \right)\times \left( 10\times 10\times 10 \right)$
We can write the right hand side value in exponent form as follows,
$\Rightarrow 1000000={{10}^{3}}\times {{10}^{3}}$
Now take cube root we get,
$\Rightarrow \sqrt[3]{1000000}=\sqrt[3]{{{10}^{3}}\times {{10}^{3}}}$
$\Rightarrow \sqrt[3]{1000000}=10\times 10$
So we get,
$\therefore \sqrt[3]{1000000}=100$
So we get the answer as$100$ .

Hence the cube root of $1000000$ is $100$.

Note: Cube root of any number $'a'$ is the number $'b'$ which satisfies the equation ${{b}^{3}}=a$ . We can also write it as $a=\sqrt[3]{b}$ . When we multiply any number three times by itself we get the cube of that number and the cube root is the inverse process of it. There are many perfect cube numbers which give an integer when we find the cube root of them but if they are not a perfect cube it gets a little complicated to find their cube root. Division method is easy when we can find the factor of the number without much calculation. Factorization or Prime Factorization is also a common method for finding the cube root of any number.