Cube Roots

If the volume of a cube is 125 cm3, what would be the length of its side? To get the length of the side of the cube, we need to know a number whose cube is 125.

Finding the square root, as you know, is the inverse operation of squaring.

Similarly, finding the cube root is the inverseproportion operation of finding cube.

We know that 23 =

So, we say that the cube root of 8 is .

We write 38 = 2. The symbol 3 denotes ‘cube-root.’

Consider the following:

Cube root through prime factorisation method

Consider 3375. Let's find its cube root using prime factorisation:

3375 = × × × × ×

= 33×53=3×53

Therefore, cube root of:

3375 = 33375 = × = (Enter factors in increasing order)

Similarly, to find 374088:

74088 = × × × × × × × × (Enter factors in increasing order)

= 23×33×73=2×3×73

Therefore,

374088 = × × =

Example 6: Find the cube root of 8000

Prime factorisation of 8000 = × × × × × × × × (Enter factors in increasing order)

So,

38000 = 2 × 2 × 5 =

Example 7: Find the cube root of 13824 by prime factorisation method.

13824 = × × × × × × × × × × × (Enter factors in increasing order)

= 23×23×23×33

Therefore,

313824= 2 × 2 × 2 × 3 =

Think, Discuss and Write

State true or false: for any integer m, m2 < m3. Why?

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