What is the square root of 2, 3 and 5?

Rounded to 4 decimal places, √2 = 1.4142, √3 = 1.7321 and √5 = 2.2361. None of them can be written as a ratio of two whole numbers. Their decimals never end, so every value you see in a chart is rounded.

Which numbers from 1 to 100 are perfect squares?

There are 10: 1, 4, 9, 16, 25, 36, 49, 64, 81, 100. Each is a whole number times itself, so its square root is a whole number. The perfect squares only filter on the chart tab shows them in a short list.

How do I simplify √72 and √50?

Split off the largest perfect square factor. √72 = √(36 × 2) = 6√2, and √50 = √(25 × 2) = 5√2. The simplified radicals tab lists the simplest form of every non-perfect square from 1 to 100.

How can I estimate a square root without a calculator?

Find the two perfect squares around the number. For √87, 9² = 81 and 10² = 100, so the root is between 9 and 10. Then average a guess with the number divided by the guess: (9 + 87/9) / 2 = 9.3333, against an exact 9.3274.

Can you take the square root of a negative number?

Not in the real numbers, because a real number squared is never negative. In complex numbers, √(−n) = i√n, so √(−9) = 3i. The calculator shows that form when you enter a negative whole number.

Can I print the square root chart for free?

Yes. The Printables tab exports the 1 to 100 and 101 to 200 charts, the perfect squares sheet, the simplified radicals sheet and the estimating sheet as PNG, SVG or print, on A4 or US Letter, in color or black and white. Everything is free and needs no account.

Math Reference

Square Root Chart

Square root chart 1 to 100 (and to 1000) with perfect squares, simplified radical form, a square root calculator and printable A4 and Letter sheets.

Roots of 1 to 1000 to 2, 3, 4 or 6 decimal placesPerfect squares and simplified radical formCalculator for any whole number up to a trillionPNG, SVG and print sheets, A4 or Letter, no sign-up

Range

Decimal places

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Rounded half up to 4 decimal places. Perfect squares show a whole number. The last column is the simplest radical form.

Square roots of 1 to 100
n	√n	Simplest form
1	1
2	1.4142	√2
3	1.7321	√3
4	2
5	2.2361	√5
6	2.4495	√6
7	2.6458	√7
8	2.8284	2√2
9	3
10	3.1623	√10
11	3.3166	√11
12	3.4641	2√3
13	3.6056	√13
14	3.7417	√14
15	3.8730	√15
16	4
17	4.1231	√17
18	4.2426	3√2
19	4.3589	√19
20	4.4721	2√5
21	4.5826	√21
22	4.6904	√22
23	4.7958	√23
24	4.8990	2√6
25	5
26	5.0990	√26
27	5.1962	3√3
28	5.2915	2√7
29	5.3852	√29
30	5.4772	√30
31	5.5678	√31
32	5.6569	4√2
33	5.7446	√33
34	5.8310	√34
35	5.9161	√35
36	6
37	6.0828	√37
38	6.1644	√38
39	6.2450	√39
40	6.3246	2√10
41	6.4031	√41
42	6.4807	√42
43	6.5574	√43
44	6.6332	2√11
45	6.7082	3√5
46	6.7823	√46
47	6.8557	√47
48	6.9282	4√3
49	7
50	7.0711	5√2
51	7.1414	√51
52	7.2111	2√13
53	7.2801	√53
54	7.3485	3√6
55	7.4162	√55
56	7.4833	2√14
57	7.5498	√57
58	7.6158	√58
59	7.6811	√59
60	7.7460	2√15
61	7.8102	√61
62	7.8740	√62
63	7.9373	3√7
64	8
65	8.0623	√65
66	8.1240	√66
67	8.1854	√67
68	8.2462	2√17
69	8.3066	√69
70	8.3666	√70
71	8.4261	√71
72	8.4853	6√2
73	8.5440	√73
74	8.6023	√74
75	8.6603	5√3
76	8.7178	2√19
77	8.7750	√77
78	8.8318	√78
79	8.8882	√79
80	8.9443	4√5
81	9
82	9.0554	√82
83	9.1104	√83
84	9.1652	2√21
85	9.2195	√85
86	9.2736	√86
87	9.3274	√87
88	9.3808	2√22
89	9.4340	√89
90	9.4868	3√10
91	9.5394	√91
92	9.5917	2√23
93	9.6437	√93
94	9.6954	√94
95	9.7468	√95
96	9.7980	4√6
97	9.8489	√97
98	9.8995	7√2
99	9.9499	3√11
100	10

Free Square Root Charts and Printables

Every sheet below is drawn from the same computed values as the tables above. View, download and print them free, no sign-up.

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Square Root Chart 1 to 100

All 100 roots to 4 decimal places with perfect squares shaded and radical forms.

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Charts

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Study aids

What is a square root?

The square root of a number n is a number that gives n when you multiply it by itself. Since 8 × 8 = 64, the square root of 64 is 8, written √64 = 8. Most square roots are not whole numbers. They are irrational: the decimal never ends and never repeats. √2 = 1.4142, √3 = 1.7321 and √5 = 2.2361 are all rounded to 4 places in the chart, and each rounded value is slightly off. Between 1 and 100 exactly 10 numbers have a whole-number root, and the other 90 are irrational.

Perfect squares chart

A perfect square is a whole number times itself: 1, 4, 9, 16, 25 and so on. The perfect squares tab lists 1² to 50², and the printable sheet covers 1² to 30², which runs up to 900. The squares grow by consecutive odd numbers: 1 + 3 = 4, 4 + 5 = 9, 9 + 7 = 16. A perfect square never ends in 2, 3, 7 or 8, which is a quick way to rule a number out. The 50th square is 2500, so √2500 = 50.

How to simplify a square root

To simplify a square root, find the largest perfect square that divides the number and take it out of the root. For √72, the largest square factor is 36, so √72 = √(36 × 2) = 6√2, which is about 8.4853. The same steps give √50 = 5√2, √48 = 4√3, √98 = 7√2 and √200 = 10√2.
A root is already in simplest form when the number has no square factor, like √2. Of the 90 non-perfect squares up to 100, 30 simplify. The calculator tab finds the factors by exact whole-number division and shows the check a² × b = n, so you can see that the result is right.

How to estimate a square root without a calculator

Bracket the number between two perfect squares. For √50, 7² = 49 and 8² = 64, so the root is between 7 and 8. Because 50 is just above 49, the answer is close to 7. A straight-line guess puts √50 at 7.0667.
For a sharper value, take one Newton step: average your starting guess with the number divided by that guess. Starting at 7, (7 + 50/7) / 2 = 7.0714, against an exact 7.0711. For √87 the same step gives 9.3333, and for √40 it gives 6.3333, close to 6.3246.

Square roots of negative numbers

No real number multiplied by itself is negative, so the square root of a negative number is not a real number. In the complex numbers, √(−n) = i√n, where i is defined by i² = −1. For example √(−16) = 4i. If you enter a negative number in the calculator, it shows this complex result instead of an error.

Square roots 1 to 1000 and printable sheets

The chart tab works as a square root table for 1 to 1000: it shows ten blocks of 100 numbers, with 2, 3, 4 or 6 decimal places. All values are computed from exact whole-number arithmetic, rounded half up, so a root like √2 is 1.414214 to 6 places with no floating-point drift. The Printables tab exports the 1 to 100 and 101 to 200 charts, the perfect squares sheet, the radicals sheet and the estimating sheet as PNG, SVG or print, on A4 or US Letter, in color or black and white.

Frequently Asked Questions

To see the perfect squares as a grid, use the multiplication chart generator. For a 1 to 100 grid, try the hundreds chart generator, and to place roots on a line use the number line generator. Looking for primes? See the prime numbers chart.