## Cube Roots Sample Problems For IBPS

Dear Reader,

Below are four problems based on simple calculations of cube root of a number.

**Question 1**

The cube root of 74088 is:

a) 47 b) 42 c) 37 d) 52

**Answer :** b) 42

Solution :

Method to find a cube root of a number:

Resolve the given numbers as the product of prime factors and take the product of prime factors, choosing out one among three of the same prime factors.

Now, resolving 74088 as the product of prime factors,

i.e., 74088 = 6 x 6 x 6 x 7 x 7 x 7 = 6^{3} x 7^{3}

Then the cube root of 74088 = 74088^{(1/3)} = (6^{3} x 7^{3})^{1/3}

6x7 = 42

Hence the answer is 42.

**Question 2**

Find the cube root of the mixed number 1 127/216.

a) 1 1/6 b) 4/6 c) 1 5/6 d) 3/6

**Answer :** a) 1 1/6

Solution :

We have to find (1 127/216)^{1/3}

(1 127/216)^{1/3} = (343/216)^{1/3}

= [(7 x 7 x 7)/(6 x 6 x 6)]^{1/3}

= [7^{3} / 6^{3}]^{1/3}

= 7/6

= 1 1/6

Hence the answer is 1 1/6.

**Question 3**

Find the least number that is multiplied by 3969 to get a number which is a perfect cube:

a) 65 b) 72 c) 63 d) 78

**Answer :** c) 63

Solution:

Resolving the given 3969 as a product of prime factors as

3969 = 7 x 7 x 9 x 9 = 7^{2} x 9^{2}

To make a number perfect cube, we have to multiply that number by the least number (7 x 9).

(7 x 9) x 7^{2} x 9^{2} = 3969 x (7 x 9)

7^{3} x 93 = 3969 x 63

Hence, the answer is 63

**Question 4**

Find the least number which is used to multiply (4^{2} x 3^{3} x 6) to get a perfect cube

a) 120 b) 144 c) 169 d) 216

**Answer :** b) 144

Solution :

Given number is 4^{2} x 3^{3} x 6

i.e., 4 x 4 x 3 x 3 x 3 x 6

If we multiply the above by 4 x 6 x 6 then we have the nearest cube (4^{3} x 3^{3} x 6^{3}) of the given number.

Hence, the answer is 4 x 6 x 6 = 144.