Squares of Numbers 11–30

Trick / Shortcut

Topic

Squares & Cubes

How It Works

For numbers between 11 and 30, memorizing their squares is the most efficient method for competitive exams. Direct recall saves significant time.

Alternatively, you can use algebraic identities for approximation or cross-checking:

Choose a nearby round number for $a$ (e.g., 20, 25, 30) and $b$ as the difference.

Reference Table for Quick Recall:

$n$	$n^2$	$n$	$n^2$
11	121	21	441
12	144	22	484
13	169	23	529
14	196	24	576
15	225	25	625
16	256	26	676
17	289	27	729
18	324	28	784
19	361	29	841
20	400	30	900

Example

$17^2$: Direct recall from memory: $\textbf{289}$

$24^2$: Direct recall from memory: $\textbf{576}$

Alternative for $24^2$ using $(a-b)^2$: $24^2 = (25-1)^2$ $= 25^2 - 2(25)(1) + 1^2$ $= 625 - 50 + 1 = \textbf{576} \checkmark$

$n$	$n^2$	$n$	$n^2$
11	121	21	441
12	144	22	484
13	169	23	529
14	196	24	576
15	225	25	625
16	256	26	676
17	289	27	729
18	324	28	784
19	361	29	841
20	400	30	900

$n$	$n^2$	$n$	$n^2$
11	121	21	441
12	144	22	484
13	169	23	529
14	196	24	576
15	225	25	625
16	256	26	676
17	289	27	729
18	324	28	784
19	361	29	841
20	400	30	900

$n$	$n^2$	$n$	$n^2$
11	121	21	441
12	144	22	484
13	169	23	529
14	196	24	576
15	225	25	625
16	256	26	676
17	289	27	729
18	324	28	784
19	361	29	841
20	400	30	900