Square Root Table

A Square Root Table is an invaluable tool in mathematics that provides the square roots of numbers, facilitating quicker computation and deeper understanding of both rational and irrational numbers. This resource is integers in algebra and other mathematical disciplines, where knowledge of square and square roots simplifies complex calculations and problem-solving. Additionally, such tables are useful in statistical analyses and the least squares method, helping to accurately model data and predict outcomes. By offering immediate access to square roots, these tables enhance learning and application in various mathematical contexts, from basic arithmetic to advanced numerical analysis.

Square Root

A square root of a number is a value that, when multiplied by itself, equals the original number. It’s represented symbolically as √, with the number of interest under the radical sign. Square roots are fundamental in various mathematical d

Square Root Table From 1 to 200

Number	Square Root (√)
√1	1.00
√2	1.41
√3	1.73
√4	2.00
√5	2.24
√6	2.45
√7	2.65
√8	2.83
√9	3.00
√10	3.16
√11	3.32
√12	3.46
√13	3.61
√14	3.74
√15	3.87
√16	4.00
√17	4.12
√18	4.24
√19	4.36
√20	4.47
√21	4.58
√22	4.69
√23	4.80
√24	4.90
√25	5.00
√26	5.10
√27	5.20
√28	5.29
√29	5.39
√30	5.48
√31	5.57
√32	5.66
√33	5.74
√34	5.83
√35	5.92
√36	6.00
√37	6.08
√38	6.16
√39	6.24
√40	6.32
√41	6.40
√42	6.48
√43	6.56
√44	6.63
√45	6.71
√46	6.78
√47	6.86
√48	6.93
√49	7.00
√50	7.07
√51	7.14
√52	7.21
√53	7.28
√54	7.35
√55	7.42
√56	7.48
√57	7.55
√58	7.62
√59	7.68
√60	7.75
√61	7.81
√62	7.87
√63	7.94
√64	8.00
√65	8.06
√66	8.12
√67	8.19
√68	8.25
√69	8.31
√70	8.37
√71	8.43
√72	8.49
√73	8.54
√74	8.60
√75	8.66
√76	8.72
√77	8.77
√78	8.83
√79	8.89
√80	8.94
√81	9.00
√82	9.06
√83	9.11
√84	9.17
√85	9.22
√86	9.27
√87	9.33
√88	9.38
√89	9.43
√90	9.49
√91	9.54
√92	9.59
√93	9.64
√94	9.70
√95	9.75
√96	9.80
√97	9.85
√98	9.90
√99	9.95
√100	10.00
√101	10.05
√102	10.10
√103	10.15
√104	10.20
√105	10.25
√106	10.30
√107	10.35
√108	10.39
√109	10.44
√110	10.49
√111	10.54
√112	10.58
√113	10.63
√114	10.68
√115	10.72
√116	10.77
√117	10.82
√118	10.86
√119	10.91
√120	10.95
√121	11.00
√122	11.04
√123	11.09
√124	11.13
√125	11.18
√126	11.22
√127	11.27
√128	11.31
√129	11.36
√130	11.40
√131	11.44
√132	11.49
√133	11.53
√134	11.58
√135	11.62
√136	11.66
√137	11.71
√138	11.75
√139	11.79
√140	11.84
√141	11.88
√142	11.92
√143	11.96
√144	12.00
√145	12.04
√146	12.08
√147	12.13
√148	12.17
√149	12.21
√150	12.25
√151	12.29
√152	12.33
√153	12.37
√154	12.41
√155	12.45
√156	12.49
√157	12.53
√158	12.57
√159	12.61
√160	12.65
√161	12.69
√162	12.73
√163	12.77
√164	12.81
√165	12.85
√166	12.89
√167	12.92
√168	12.96
√169	13.00
√170	13.04
√171	13.08
√172	13.11
√173	13.15
√174	13.19
√175	13.23
√176	13.26
√177	13.30
√178	13.34
√179	13.38
√180	13.41
√181	13.45
√182	13.49
√183	13.52
√184	13.56
√185	13.60
√186	13.63
√187	13.67
√188	13.70
√189	13.74
√190	13.78
√191	13.81
√192	13.85
√193	13.88
√194	13.92
√195	13.95
√196	14.00
√197	14.03
√198	14.07
√199	14.10
√200	14.14

More About Square Root Table

Square Root of 1	Square Root of 2	Square Root of 3	Square Root of 4	Square Root of 5
Square Root of 6	Square Root of 7	Square Root of 8	Square Root of 9	Square Root of 10
Square Root of 11	Square Root of 12	Square Root of 13	Square Root of 14	Square Root of 15
Square Root of 16	Square Root of 17	Square Root of 18	Square Root of 19	Square Root of 20
Square Root of 21	Square Root of 22	Square Root of 23	Square Root of 24	Square Root of 25
Square Root of 26	Square Root of 27	Square Root of 28	Square Root of 29	Square Root of 30
Square Root of 31	Square Root of 32	Square Root of 33	Square Root of 34	Square Root of 35
Square Root of 36	Square Root of 37	Square Root of 38	Square Root of 39	Square Root of 40
Square Root of 41	Square Root of 42	Square Root of 43	Square Root of 44	Square Root of 45
Square Root of 46	Square Root of 47	Square Root of 48	Square Root of 49	Square Root of 50
Square Root of 51	Square Root of 52	Square Root of 53	Square Root of 54	Square Root of 55
Square Root of 56	Square Root of 57	Square Root of 58	Square Root of 59	Square Root of 60
Square Root of 61	Square Root of 62	Square Root of 63	Square Root of 64	Square Root of 65
Square Root of 66	Square Root of 67	Square Root of 68	Square Root of 69	Square Root of 70
Square Root of 71	Square Root of 72	Square Root of 73	Square Root of 74	Square Root of 75
Square Root of 76	Square Root of 77	Square Root of 78	Square Root of 79	Square Root of 80
Square Root of 81	Square Root of 82	Square Root of 83	Square Root of 84	Square Root of 85
Square Root of 86	Square Root of 87	Square Root of 88	Square Root of 89	Square Root of 90
Square Root of 91	Square Root of 92	Square Root of 93	Square Root of 94	Square Root of 95
Square Root of 96	Square Root of 97	Square Root of 98	Square Root of 99	Square Root of 100

Even Numbers of Square Root Table

Number	Square Root (√)
√2	1.41
√4	2.00
√6	2.45
√8	2.83
√10	3.16
√12	3.46
√14	3.74
√16	4.00
√18	4.24
√20	4.47
√22	4.69
√24	4.90
√26	5.10
√28	5.29
√30	5.48
√32	5.66
√34	5.83
√36	6.00
√38	6.16
√40	6.32
√42	6.48
√44	6.63
√46	6.78
√48	6.93
√50	7.07
√52	7.21
√54	7.35
√56	7.48
√58	7.62
√60	7.75
√62	7.87
√64	8.00
√66	8.12
√68	8.25
√70	8.37
√72	8.49
√74	8.60
√76	8.72
√78	8.83
√80	8.94
√82	9.06
√84	9.17
√86	9.27
√88	9.38
√90	9.49
√92	9.59
√94	9.70
√96	9.80
√98	9.90
√100	10.00
√102	10.10
√104	10.20
√106	10.30
√108	10.39
√110	10.49
√112	10.58
√114	10.68
√116	10.77
√118	10.86
√120	10.95
√122	11.04
√124	11.13
√126	11.22
√128	11.31
√130	11.40
√132	11.49
√134	11.58
√136	11.66
√138	11.75
√140	11.84
√142	11.92
√144	12.00
√146	12.08
√148	12.17
√150	12.25
√152	12.33
√154	12.41
√156	12.49
√158	12.57
√160	12.65
√162	12.73
√164	12.81
√166	12.89
√168	12.96
√170	13.04
√172	13.11
√174	13.19
√176	13.26
√178	13.34
√180	13.41
√182	13.49
√184	13.56
√186	13.63
√188	13.70
√190	13.78
√192	13.85
√194	13.92
√196	14.00
√198	14.07
√200	14.14

Odd Numbers of Square Root Table

Number	Square Root (Approx.)
√1	1.00
√3	1.73
√5	2.24
√7	2.65
√9	3.00
√11	3.32
√13	3.61
√15	3.87
√17	4.12
√19	4.36
√21	4.58
√23	4.80
√25	5.00
√27	5.20
√29	5.39
√31	5.57
√33	5.74
√35	5.92
√37	6.08
√39	6.24
√41	6.40
√43	6.56
√45	6.71
√47	6.86
√49	7.00
√51	7.14
√53	7.28
√55	7.42
√57	7.55
√59	7.68
√61	7.81
√63	7.94
√65	8.06
√67	8.19
√69	8.31
√71	8.43
√73	8.54
√75	8.66
√77	8.77
√79	8.89
√81	9.00
√83	9.11
√85	9.22
√87	9.33
√89	9.43
√91	9.54
√93	9.64
√95	9.75
√97	9.85
√99	9.95
√101	10.05
√103	10.15
√105	10.25
√107	10.35
√109	10.44
√111	10.54
√113	10.63
√115	10.72
√117	10.82
√119	10.91
√121	11.00
√123	11.09
√125	11.18
√127	11.27
√129	11.36
√131	11.44
√133	11.53
√135	11.62
√137	11.71
√139	11.79
√141	11.88
√143	11.96
√145	12.04
√147	12.13
√149	12.21
√151	12.29
√153	12.37
√155	12.45
√157	12.53
√159	12.61
√161	12.69
√163	12.77
√165	12.85
√167	12.92
√169	13.00
√171	13.08
√173	13.15
√175	13.23
√177	13.30
√179	13.38
√181	13.45
√183	13.52
√185	13.60
√187	13.67
√189	13.74
√191	13.81
√193	13.88
√195	13.95
√197	14.03
√199	14.10

Perfect Squares of Square Root Table

Number	Square Root (√)
√1	1
√4	2
√9	3
√16	4
√25	5
√36	6
√49	7
√64	8
√81	9
√100	10
√121	11
√144	12
√169	13
√196	14

Non-Perfect Squares of Square Root Table

Number	Square Root (√)
√2	1.41
√3	1.73
√5	2.24
√6	2.45
√7	2.65
√8	2.83
√10	3.16
√11	3.32
√12	3.46
√13	3.61
√14	3.74
√15	3.87
√17	4.12
√18	4.24
√19	4.36
√20	4.47
√21	4.58
√22	4.69
√23	4.80
√24	4.90
√26	5.10
√27	5.20
√28	5.29
√29	5.39
√30	5.48
√31	5.57
√32	5.66
√33	5.74
√34	5.83
√35	5.92
√37	6.08
√38	6.16
√39	6.24
√40	6.32
√41	6.40
√42	6.48
√43	6.56
√44	6.63
√45	6.71
√46	6.78
√47	6.86
√48	6.93
√50	7.07
√51	7.14
52	7.21
√53	7.28
√54	7.35
√55	7.42
√56	7.48
√57	7.55
√58	7.62
√59	7.68
√60	7.75
√61	7.81
√62	7.87
√63	7.94
√65	8.06
√66	8.12
√67	8.19
√68	8.25
√69	8.31
√70	8.37
√71	8.43
√72	8.49
√73	8.54
√74	8.60
√75	8.66
√76	8.72
√77	8.77
√78	8.83
√79	8.89
√80	8.94
√82	9.06
√83	9.11
√84	9.17
√85	9.22
√86	9.27
√87	9.33
√88	9.38
√89	9.43
√90	9.49
√91	9.54
√92	9.59
√93	9.64
√94	9.70
√95	9.75
√96	9.80
√97	9.85
√98	9.90
√99	9.95
√101	10.05
√102	10.10
√103	10.15
√104	10.20
√105	10.25
√106	10.30
√107	10.35
√108	10.39
√109	10.44
√110	10.49
√111	10.54
√112	10.58
√113	10.63
√114	10.68
√115	10.72
√116	10.77
√117	10.82
√118	10.86
√119	10.91
√120	10.95
√122	11.04
√123	11.09
√124	11.13
√125	11.18
√126	11.22
√127	11.27
√128	11.31
√129	11.36
√130	11.40
√131	11.44
√132	11.49
√133	11.53
√134	11.58
√135	11.62
√136	11.66
√137	11.71
√138	11.75
√139	11.79
√140	11.84
√141	11.88
√142	11.92
√143	11.96
√145	12.04
√146	12.08
√147	12.13
√148	12.17
√149	12.21
√150	12.25
√151	12.29
√152	12.33
√153	12.37
√154	12.41
√155	12.45
√156	12.49
√157	12.53
√158	12.57
√159	12.61
√160	12.65
√161	12.69
√162	12.73
√163	12.77
√164	12.81
√165	12.85
√166	12.89
√167	12.92
√168	12.96
√170	13.04
√171	13.08
√172	13.11
√173	13.15
√174	13.19
√175	13.23
√176	13.26
√177	13.30
√178	13.34
√179	13.38
√180	13.41
√181	13.45
√182	13.49
√183	13.52
√184	13.56
√185	13.60
√186	13.63
√187	13.67
√188	13.70
√189	13.74
√190	13.78
√191	13.81
√192	13.85
√193	13.88
√194	13.92
√195	13.95
√197	14.03
√198	14.07
√199	14.10
√200	14.14

Properties of the Square Root Table

A square root table is a valuable mathematical resource that provides quick access to square root values of numbers. Understanding its properties can enhance its utilization in various mathematical contexts, from elementary education to advanced studies. Here are some key properties and characteristics of a square root table:

Incremental Values

• The square root table lists numbers and their corresponding square roots in a sequential manner. As the numbers increase, their square roots also increase, but the rate of increase gradually slows down. This is because the function 𝑓(𝑥) = √𝑥 is a concave function, meaning as 𝑥 increases, the rate of change of 𝑥 decreases.

Rational and Irrational Values

The table includes both rational and irrational numbers. Square roots of perfect squares (like 1, 4, 9, 16, …) are rational, whereas square roots of non-perfect squares (like 2, 3, 5, …) are irrational. This highlights the diversity of number types in algebra and provides a practical demonstration of rational versus irrational numbers.

Symmetry and Patterns

• Square root values exhibit symmetry around certain points. For example, the difference in square root values between successive squares (like between 1 and 4, 4 and 9, 9 and 16) decreases as numbers get larger. This pattern helps in estimating square roots of numbers that are not listed in the table.

Practical Application in Estimation

• The table can be used for estimating square roots of numbers that are not perfect squares. By locating the two nearest perfect square roots, users can interpolate to estimate the square root of a given number, which is particularly useful in numerical and engineering fields.

Utility in Education and Problem Solving

• Square root tables are excellent educational tools, helping students understand the concept of square roots without the need for calculative aids. They also serve as a quick reference in problem-solving situations, especially in exams or when computational devices are not available.

Historical Relevance

• Before the widespread availability of calculators and computers, square root tables were essential in many scientific and engineering calculations. They represent an important historical aspect of computational mathematics.

Basis for Advanced Mathematical Concepts

• Understanding the properties and patterns in square root values can lead to deeper insights into more complex mathematical theories, such as quadratic equations, the Pythagorean theorem, and calculus. It also ties into statistical methods like the least squares method used for data fitting and prediction.

FAQs

Are square root tables still relevant with the availability of digital tools?

While digital tools like calculators and software have largely replaced the need for manual lookup tables in practical applications, square root tables still hold educational value. They help students understand the concept of square roots and number properties more concretely and provide a historical perspective on mathematical computations.

Can square root tables help with understanding rational and irrational numbers?

Yes, square root tables help illustrate the difference between rational and irrational numbers. Square roots of perfect squares are rational numbers, while square roots of non-perfect squares are typically irrational. This contrast can be clearly seen and understood through a square root table.

What is the range of numbers covered in a typical square root table?

The range can vary depending on the table, but most educational square root tables cover numbers from 1 to at least 100 or 200. Some might go even higher to cater to more advanced mathematical applications or studies.