Question

How do you simplify $\sqrt[3]{3000}$?

Answer 1

Hint: Here we have to find the cube root of the given number. In order to find the cube root of the given number first we will represent the number by using the product of the prime factors. Then we will group the factors into a pair of three to get the desired answer.

Complete step-by-step solution:
We have been given $\sqrt[3]{3000}$.
We have to find the cube root of the given number.
We know that cube root is the reverse process of cube. Cube root of a number is a number when cubed gives the original number as a result. $\sqrt[3]{{}}$ is the symbol used to denote the cube root.
To find the cube root of $\sqrt[3]{3000}$ we need to factorize the numbers first.
Now, we can write the number 3000 as $3000=10\times 10\times 10\times 3$
Now, by grouping of three we get
$\Rightarrow \sqrt[3]{3000}=\sqrt[3]{{{10}^{3}}\times 3}$
Therefore we will get
$\Rightarrow \sqrt[3]{3000}=10\sqrt[3]{3}$
Hence the given number is not a perfect cube.
So on simplifying we get $\sqrt[3]{3000}=10\sqrt[3]{3}$.

Note: A perfect cube is defined as the number that is the product of an integers three times. If the given number is not a perfect cube then in order to simplify it we need to write it as a product of a perfect cube and other numbers. The cube root of a negative number is always negative. Students may try to remember some basic cube and cube roots of numbers.