Question

What is the cube root of 1000?

Answer 1

Hint: Now to find the cube root of 1000 we will first factorize the number into prime factors. Then we will try to write the number as a cube of some number. Hence we will get the cube root of the given number.

Complete step by step solution:
Now first let us understand the concept of exponents.
Now any number written in the form of ${{a}^{n}}$ is called exponents. Now here n is called power of a. Let us now understand what this power represents. The power raised to a number represents how many times a number is multiplied to itself. Hence if n = 4 then the number must be multiplied to itself 4 times.
Let us understand this by an example. Suppose we have an exponent ${{4}^{3}}$ then this can be written as $4\times 4\times 4=64$ .
Now cubes are the numbers which are raised to 3. Hence if we have power of any number as 3 it is called a cube of that number.
Now cube root is nothing but the inverse of cube function. Cube root of x is denoted by $\sqrt[3]{x}$ .
Now let us understand this by an example. Consider a cube of 4. ${{4}^{3}}=64$ .
Hence we have a cube of 4 is 64. Then we can say the cube root of 64 is 4.
Now consider the given number 1000.
First let us factorize the given number.
\[\begin{align}
  & \Rightarrow 1000=2\times 2\times 2\times 5\times 5\times 5 \\
 & \Rightarrow 1000=\left( 2\times 5 \right)\times \left( 2\times 5 \right)\times \left( 2\times 5 \right) \\
 & \Rightarrow 1000={{\left( 2\times 5 \right)}^{3}} \\
 & \Rightarrow 1000={{10}^{3}} \\
\end{align}\]
Now since we have $1000={{10}^{3}}$ we can say that $\sqrt[3]{1000}=10$ .
Hence we get the cube root of 1000 is 10.

Note: Now note that here we have taken n = 3 in the exponent ${{x}^{n}}$ hence the function is called cube. Similarly if we have n = 2 then the function is called square. Also note that the square of the negative number is positive but the cube of negative number is negative.