Square Roots of Numbers 1 to 1,000

How the square roots of 1 to 1,000 break down

31 of the numbers are perfect squares (1, 4, 9 … 961) with whole-number roots from 1 to 31.
362 more can be simplified because they contain a perfect-square factor, such as √72 = 6√2 or √500 = 10√5.
The remaining 607 are square-free, so their roots are already in simplest form (√2, √30, √997 …).

Perfect squares from 1 to 1,000
n	n²	n	n²	n	n²	n	n²
1	1	9	81	17	289	25	625
2	4	10	100	18	324	26	676
3	9	11	121	19	361	27	729
4	16	12	144	20	400	28	784
5	25	13	169	21	441	29	841
6	36	14	196	22	484	30	900
7	49	15	225	23	529	31	961
8	64	16	256	24	576

Highlighted numbers are perfect squares. For decimals, fractions, negative numbers or values above 1,000, use the square root calculator.

Square roots of 1–100

Perfect squares in this block: 1 (√ = 1), 4 (√ = 2), 9 (√ = 3), 16 (√ = 4), 25 (√ = 5), 36 (√ = 6), 49 (√ = 7), 64 (√ = 8), 81 (√ = 9), 100 (√ = 10). Every other root in the block lies between 1 and 10.

Square roots of 101–200

Perfect squares in this block: 121 (√ = 11), 144 (√ = 12), 169 (√ = 13), 196 (√ = 14). Every other root in the block lies between 10 and 15.

Square roots of 201–300

Perfect squares in this block: 225 (√ = 15), 256 (√ = 16), 289 (√ = 17). Every other root in the block lies between 14 and 18.

Square roots of 301–400

Perfect squares in this block: 324 (√ = 18), 361 (√ = 19), 400 (√ = 20). Every other root in the block lies between 17 and 20.

Square roots of 401–500

Perfect squares in this block: 441 (√ = 21), 484 (√ = 22). Every other root in the block lies between 20 and 23.

Square roots of 501–600

Perfect squares in this block: 529 (√ = 23), 576 (√ = 24). Every other root in the block lies between 22 and 25.

Square roots of 601–700

Perfect squares in this block: 625 (√ = 25), 676 (√ = 26). Every other root in the block lies between 24 and 27.

Square roots of 701–800

Perfect squares in this block: 729 (√ = 27), 784 (√ = 28). Every other root in the block lies between 26 and 29.

Square roots of 801–900

Perfect squares in this block: 841 (√ = 29), 900 (√ = 30). Every other root in the block lies between 28 and 30.

Square roots of 901–1,000

Perfect squares in this block: 961 (√ = 31). Every other root in the block lies between 30 and 32.

Back to the Square root calculator.

n	n²	n	n²	n	n²	n	n²
1	1	9	81	17	289	25	625
2	4	10	100	18	324	26	676
3	9	11	121	19	361	27	729
4	16	12	144	20	400	28	784
5	25	13	169	21	441	29	841
6	36	14	196	22	484	30	900
7	49	15	225	23	529	31	961
8	64	16	256	24	576

n	n²	n	n²	n	n²	n	n²
1	1	9	81	17	289	25	625
2	4	10	100	18	324	26	676
3	9	11	121	19	361	27	729
4	16	12	144	20	400	28	784
5	25	13	169	21	441	29	841
6	36	14	196	22	484	30	900
7	49	15	225	23	529	31	961
8	64	16	256	24	576

n	n²	n	n²	n	n²	n	n²
1	1	9	81	17	289	25	625
2	4	10	100	18	324	26	676
3	9	11	121	19	361	27	729
4	16	12	144	20	400	28	784
5	25	13	169	21	441	29	841
6	36	14	196	22	484	30	900
7	49	15	225	23	529	31	961
8	64	16	256	24	576