Worksheet on Squares and Cubes

Solved Questions on Squares and Cubes

1. What is the least number that must be subtracted from 2405 to make it a perfect square? 

a) 2
b) 4
c) 5
d) 7

Answer: b) 4

Explanation: Using long division method to find the square root,

Taking square root,
Quotient = 49
Perfect Square: 492 = 49 × 49
                              = 2401
Remainder = 4

So, 4 is to be subtracted from 2405.

2. If the Pythagorean triple of one member is 18, what are the other two members?

a) 80 and 81
b) 81 and 82
c) 82 and 81
d) 82 and 80

Answer: d) 82 and 80

Explanation: Pythagorean triplets is given by the formula:

2m, m² + 1, m² − 1 for any number m > 1

Let 2m = 18
⇒ m = 9

Therefore, m² + 1 = 9² + 1
                            = 81 + 1 
                             = 82

m² − 1 = 9² − 1 
             = 81 − 1 
              = 80

Hence, the other two members are 80 and 82.

3. If √2 = 1.4 and √3 = 1.7, then what is the value of √216?

a) 12.28
b) 14.28
c) 16.28
d) 18.28

Answer: b) 14.28

Explanation: √216 = √(2 × 2 × 2 × 3 × 3 × 3)
= 2 × 3 × √( 2 × 3)
= 6 × √2 × √3
= 6 × 1.4 × 1.7
= 14.28

4. Find the smallest number by which 333396 may be divided so that the quotient is a perfect cube.

a) 16
b) 26
c) 36 
d) 46

Answer: c) 36 

Explanation: Using prime factorisation method to find the cube root,

Prime factors of 333396 = 3 × 3 × 3 × 3 × 3 × 7 × 7 × 7 × 2 × 2
= (3 × 3 × 3) × (7 × 7 × 7) × 3 × 3 × 2 × 2 

Clearly, 333396 must be divided by (3 × 3 × 2 × 2)  
= 9 × 4 
= 36

5. What is the side of a cube in centimetres whose volume is 57066625 mm³?

a) 0.385 cm
b) 3.85 cm
c) 38.5 cm
d) 385 cm

Answer: b) 3.85 cm

Explanation: Volume of a cube = 57066625 mm³
⇒ (Side)³ = 57066625 mm³
⇒ Side =  ³√57066625

⇒ Side of a cube =  385 mm
⇒ Side of a cube =  385/10 cm [1 mm = 1/10 cm]
Side of a cube =  3.85 cm