## 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

## 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

## 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.