A square root table lists numbers alongside their square roots for quick reference. It helps solve mathematical problems faster and improves calculation skills. Square root tables are useful in arithmetic, algebra, and geometry.

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
Square-Root-Table-From-1-to-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.