Question

How do you find the cube roots of $1000?$

Answer 1

Hint: To solve the question we need to know the concept of roots and powers. We need to factorise the given number to find the value of the cube root of the given number. Cube root of a number is, what number should be multiplied thrice to get 1000. The formula used here is $\sqrt[3]{b}$ which is equal to a, where $b=a\times a \times a$.

Complete step-by-step solution:
To solve the given question, to find the cube root of $1000$, our first step is to prime factorise the $1000$.
We get:
$1000=2\times 5\times 2\times 5\times 2\times 5$
This is further written as
$1000=2\times 2\times 2\times 5\times 5\times 5$
These are the factors of the given number $1000$. To find the cube root of the number the factors which have come thrice will be considered single time. So mathematically it could be written as
$\sqrt[3]{1000}$
$\Rightarrow \sqrt[3]{2\times 2\times 2\times 5\times 5\times 5}$
On further calculating, we get:
$\Rightarrow 2\times 5$
$\Rightarrow 10$
$\therefore $The cube root of $1000$ is $10$.

Note: We can check whether the cube root is correct or not by multiplying the answer thrice. So on doing so , we get
$10\times 10\times 10$
$\Rightarrow 1000$
Since the number after multiplying the cube root comes to end up with the same number that is given in the question, which is $1000$. So we can infer that our answer is correct. We should always prime factorise the number to avoid errors in the solution.
In this question we were asked to find the cube root which means the power of the number is$\dfrac{1}{3}$. Similarly different questions may arise when in the similar manner we would be asked to find the square root which is $\dfrac{1}{2}$ of the number or $\dfrac{1}{4}$ of a number. For these types of questions the same procedure is followed, but the number of times the factor is considered depends upon the power.