Squares and Cubes 1 to 50 (with Shortcut Tricks)

Here is the complete list of squares and cubes 1 to 50, followed by shortcut tricks that let your child work out most of them mentally.

Knowing squares up to 30 and cubes up to 15 by heart saves real time in Class 8–10 exams, especially in square roots, Pythagoras and mensuration questions.

What Are Squares and Cubes?

The square of a number is itself multiplied by itself: 7² = 49. The cube is itself multiplied three times: 7³ = 343.

Squares and Cubes Chart: 1 to 50

No.	Square	Cube	No.	Square	Cube
1	1	1	26	676	17,576
2	4	8	27	729	19,683
3	9	27	28	784	21,952
4	16	64	29	841	24,389
5	25	125	30	900	27,000
6	36	216	31	961	29,791
7	49	343	32	1,024	32,768
8	64	512	33	1,089	35,937
9	81	729	34	1,156	39,304
10	100	1,000	35	1,225	42,875
11	121	1,331	36	1,296	46,656
12	144	1,728	37	1,369	50,653
13	169	2,197	38	1,444	54,872
14	196	2,744	39	1,521	59,319
15	225	3,375	40	1,600	64,000
16	256	4,096	41	1,681	68,921
17	289	4,913	42	1,764	74,088
18	324	5,832	43	1,849	79,507
19	361	6,859	44	1,936	85,184
20	400	8,000	45	2,025	91,125
21	441	9,261	46	2,116	97,336
22	484	10,648	47	2,209	103,823
23	529	12,167	48	2,304	110,592
24	576	13,824	49	2,401	117,649
25	625	15,625	50	2,500	125,000

Shortcut Tricks for Squares

Numbers ending in 5: multiply the tens digit by the next number, write 25 at the end. 35² → 3×4=12, then 25 → 1225. 85² → 8×9=72, then 25 → 7225.

Numbers near 50: (50+k)² = 2500 + 100k + k². 53² = 2500+300+9 = 2809; 47² = 2500−300+9 = 2209.

Using (a+b)²: 23² = 20² + 2(20)(3) + 3² = 529. See our (a + b)² formula guide.

Build from the previous square: (n+1)² = n² + n + (n+1). If 40² = 1600, then 41² = 1600+40+41 = 1681.

Facts: a perfect square never ends in 2, 3, 7 or 8. The square of an even number is even; of an odd number is odd.

Shortcut Tricks for Cubes

Last-digit pattern: a cube's last digit depends only on the number's last digit — 0→0, 1→1, 2→8, 3→7, 4→4, 5→5, 6→6, 7→3, 8→2, 9→9 (notice the swaps: 2↔8 and 3↔7).

Finding a cube root (up to 6 digits) in seconds — example 74088:

1. Last digit is 8 → from the pattern, the ones digit of the root is 2.
2. Strike off the last three digits, leaving 74.
3. Largest cube ≤ 74 is 4³ = 64 → tens digit is 4.
4. Answer: 42. Check: 42³ = 74088 ✓

Try it: cube root of 39304 — last digit 4 → ones digit 4; leftover 39 is between 3³=27 and 4³=64, so tens digit 3. Answer: 34. Check: 34³ = 39304 ✓

How Much Should Children Memorise?

Class	Suggested target
Class 6–7	Squares 1–20, cubes 1–10
Class 8	Squares 1–30, cubes 1–15
Class 9–10	Squares 1–30 by heart, tricks for the rest up to 50

Frequently Asked Questions

What is the square of 25?
625. Using the ending-in-5 trick: 2 × 3 = 6, then 25 → 625.

Can a perfect square end in 7?
No. Perfect squares can only end in 0, 1, 4, 5, 6 or 9.

How do you find the cube root of a large perfect cube?
Use the last digit to find the ones digit, then strike off the last three digits and find the largest cube below what remains for the tens digit.