In order to understand cube root, we first need to know what a cube is. A number is said to be cubed when it is used three times in multiplication. Now, cube root is the opposite of cube. Cube root is said to be the value which is cubed to give the original number to us. Like when we look at a tree we just see the trunk and the leaves but their roots can’t be seen which actually produced it. Thus, cube root is the value which produced the cube. To denote that the number is cubed, we write it as “5^3” which means that the number 5 is to be multiplied three times. Cube root is denoted by √ which is a radical symbol with small 3 to show that it is cube root.
Example 1: Find the cube of 5 and cube root of 125.
Solution: STEP 1: Multiply the number 5 three times i.e. 5 x 5 x 5 = 125
=> Therefore, 125 is the cube of 5
=> Hence, 5^3 = 125
=> STEP 2: Calculating the cube root of 125: 3√125 = 5
=> Therefore, 5 is the cube root of 125 i.e. 125= 5 x 5 x 5.
=> Since 5 appeared three times in the multiplication, thus 5 is the cube root of 125.
Example 2: Find the cube root of 64.
Solution: STEP 1: Calculating the cube root of 64: 3√64 = 4
=> Therefore, the cube root of 64 is 4 i.e. 64 = 4 x 4 x 4. Since 4 appeared three times in the multiplication, thus 4 is the cube root of 64.
=> Hence, 4 is the cube root of 64.