Squares, Cubes and Mental Maths Tricks for Competitive Exams

In a timed exam, calculation speed is a real advantage. A small set of memorised values and a few tricks removes a lot of slow arithmetic.

Squares to memorise (1 to 25)

n	n²	n	n²	n	n²
1	1	10	100	19	361
2	4	11	121	20	400
3	9	12	144	21	441
4	16	13	169	22	484
5	25	14	196	23	529
6	36	15	225	24	576
7	49	16	256	25	625
8	64	17	289
9	81	18	324

Cubes to memorise (1 to 10)

1, 8, 27, 64, 125, 216, 343, 512, 729, 1000.

Trick 1: squaring a number ending in 5

Multiply the first digit(s) by the next number, then attach 25.

• 35²: 3 × 4 = 12, so 1225.
• 65²: 6 × 7 = 42, so 4225.
• 85²: 8 × 9 = 72, so 7225.

Trick 2: squares near 100

Use (100 − a)² = 10000 − 200a + a².

• 98²: a = 2, so 10000 − 400 + 4 = 9604.
• 97²: a = 3, so 10000 − 600 + 9 = 9409.

Trick 3: multiplying by 11

Write the digits with their sum in the middle.

• 43 × 11: 4, (4 + 3), 3 gives 473.
• 52 × 11: 5, (5 + 2), 2 gives 572.
• If the middle sum exceeds 9, carry: 78 × 11: 7, (7 + 8 = 15), 8. Carry the 1 to get 858.

Trick 4: the identity (a + b)(a − b) = a² − b²

• 52 × 48 = (50 + 2)(50 − 2) = 2500 − 4 = 2496.
• 103 × 97 = 100² − 3² = 9991.

Divisibility rules

Divisor	Rule
2	last digit even
3	digit sum divisible by 3
4	last two digits divisible by 4
5	last digit 0 or 5
9	digit sum divisible by 9
11	the difference between the sums of alternate digits is 0 or a multiple of 11

Practice habit

Spend five minutes daily on tables and tricks, and short MCQ sessions will feel faster.

Practise with Online Exam Question & Answer →