Square Root Table – Table, Values, Properties, FAQs

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Created by: Team Maths - Examples.com, Last Updated: July 29, 2024

Square Root Table – Table, Values, Properties, FAQs

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

NumberSquare Root (√)
√11.00
√21.41
√31.73
√42.00
√52.24
√62.45
√72.65
√82.83
√93.00
√103.16
√113.32
√123.46
√133.61
√143.74
√153.87
√164.00
√174.12
√184.24
√194.36
√204.47
√214.58
√224.69
√234.80
√244.90
√255.00
√265.10
√275.20
√285.29
√295.39
√305.48
√315.57
√325.66
√335.74
√345.83
√355.92
√366.00
√376.08
√386.16
√396.24
√406.32
√416.40
√426.48
√436.56
√446.63
√456.71
√466.78
√476.86
√486.93
√497.00
√507.07
√517.14
√527.21
√537.28
√547.35
√557.42
√567.48
√577.55
√587.62
√597.68
√607.75
√617.81
√627.87
√637.94
√648.00
√658.06
√668.12
√678.19
√688.25
√698.31
√708.37
√718.43
√728.49
√738.54
√748.60
√758.66
√768.72
√778.77
√788.83
√798.89
√808.94
√819.00
√829.06
√839.11
√849.17
√859.22
√869.27
√879.33
√889.38
√899.43
√909.49
√919.54
√929.59
√939.64
√949.70
√959.75
√969.80
√979.85
√989.90
√999.95
√10010.00
√10110.05
√10210.10
√10310.15
√10410.20
√10510.25
√10610.30
√10710.35
√10810.39
√10910.44
√11010.49
√11110.54
√11210.58
√11310.63
√11410.68
√11510.72
√11610.77
√11710.82
√11810.86
√11910.91
√12010.95
√12111.00
√12211.04
√12311.09
√12411.13
√12511.18
√12611.22
√12711.27
√12811.31
√12911.36
√13011.40
√13111.44
√13211.49
√13311.53
√13411.58
√13511.62
√13611.66
√13711.71
√13811.75
√13911.79
√14011.84
√14111.88
√14211.92
√14311.96
√14412.00
√14512.04
√14612.08
√14712.13
√14812.17
√14912.21
√15012.25
√15112.29
√15212.33
√15312.37
√15412.41
√15512.45
√15612.49
√15712.53
√15812.57
√15912.61
√16012.65
√16112.69
√16212.73
√16312.77
√16412.81
√16512.85
√16612.89
√16712.92
√16812.96
√16913.00
√17013.04
√17113.08
√17213.11
√17313.15
√17413.19
√17513.23
√17613.26
√17713.30
√17813.34
√17913.38
√18013.41
√18113.45
√18213.49
√18313.52
√18413.56
√18513.60
√18613.63
√18713.67
√18813.70
√18913.74
√19013.78
√19113.81
√19213.85
√19313.88
√19413.92
√19513.95
√19614.00
√19714.03
√19814.07
√19914.10
√20014.14

More About Square Root Table

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

Even Numbers of Square Root Table

NumberSquare Root (√)
√21.41
√42.00
√62.45
√82.83
√103.16
√123.46
√143.74
√164.00
√184.24
√204.47
√224.69
√244.90
√265.10
√285.29
√305.48
√325.66
√345.83
√366.00
√386.16
√406.32
√426.48
√446.63
√466.78
√486.93
√507.07
√527.21
√547.35
√567.48
√587.62
√607.75
√627.87
√648.00
√668.12
√688.25
√708.37
√728.49
√748.60
√768.72
√788.83
√808.94
√829.06
√849.17
√869.27
√889.38
√909.49
√929.59
√949.70
√969.80
√989.90
√10010.00
√10210.10
√10410.20
√10610.30
√10810.39
√11010.49
√11210.58
√11410.68
√11610.77
√11810.86
√12010.95
√12211.04
√12411.13
√12611.22
√12811.31
√13011.40
√13211.49
√13411.58
√13611.66
√13811.75
√14011.84
√14211.92
√14412.00
√14612.08
√14812.17
√15012.25
√15212.33
√15412.41
√15612.49
√15812.57
√16012.65
√16212.73
√16412.81
√16612.89
√16812.96
√17013.04
√17213.11
√17413.19
√17613.26
√17813.34
√18013.41
√18213.49
√18413.56
√18613.63
√18813.70
√19013.78
√19213.85
√19413.92
√19614.00
√19814.07
√20014.14

Odd Numbers of Square Root Table

NumberSquare Root (Approx.)
√11.00
√31.73
√52.24
√72.65
√93.00
√113.32
√133.61
√153.87
√174.12
√194.36
√214.58
√234.80
√255.00
√275.20
√295.39
√315.57
√335.74
√355.92
√376.08
√396.24
√416.40
√436.56
√456.71
√476.86
√497.00
√517.14
√537.28
√557.42
√577.55
√597.68
√617.81
√637.94
√658.06
√678.19
√698.31
√718.43
√738.54
√758.66
√778.77
√798.89
√819.00
√839.11
√859.22
√879.33
√899.43
√919.54
√939.64
√959.75
√979.85
√999.95
√10110.05
√10310.15
√10510.25
√10710.35
√10910.44
√11110.54
√11310.63
√11510.72
√11710.82
√11910.91
√12111.00
√12311.09
√12511.18
√12711.27
√12911.36
√13111.44
√13311.53
√13511.62
√13711.71
√13911.79
√14111.88
√14311.96
√14512.04
√14712.13
√14912.21
√15112.29
√15312.37
√15512.45
√15712.53
√15912.61
√16112.69
√16312.77
√16512.85
√16712.92
√16913.00
√17113.08
√17313.15
√17513.23
√17713.30
√17913.38
√18113.45
√18313.52
√18513.60
√18713.67
√18913.74
√19113.81
√19313.88
√19513.95
√19714.03
√19914.10

Perfect Squares of Square Root Table

NumberSquare Root (√)
√11
√42
√93
√164
√255
√366
√497
√648
√819
√10010
√12111
√14412
√16913
√19614

Non-Perfect Squares of Square Root Table

NumberSquare Root (√)
√21.41
√31.73
√52.24
√62.45
√72.65
√82.83
√103.16
√113.32
√123.46
√133.61
√143.74
√153.87
√174.12
√184.24
√194.36
√204.47
√214.58
√224.69
√234.80
√244.90
√265.10
√275.20
√285.29
√295.39
√305.48
√315.57
√325.66
√335.74
√345.83
√355.92
√376.08
√386.16
√396.24
√406.32
√416.40
√426.48
√436.56
√446.63
√456.71
√466.78
√476.86
√486.93
√507.07
√517.14
527.21
√537.28
√547.35
√557.42
√567.48
√577.55
√587.62
√597.68
√607.75
√617.81
√627.87
√637.94
√658.06
√668.12
√678.19
√688.25
√698.31
√708.37
√718.43
√728.49
√738.54
√748.60
√758.66
√768.72
√778.77
√788.83
√798.89
√808.94
√829.06
√839.11
√849.17
√859.22
√869.27
√879.33
√889.38
√899.43
√909.49
√919.54
√929.59
√939.64
√949.70
√959.75
√969.80
√979.85
√989.90
√999.95
√10110.05
√10210.10
√10310.15
√10410.20
√10510.25
√10610.30
√10710.35
√10810.39
√10910.44
√11010.49
√11110.54
√11210.58
√11310.63
√11410.68
√11510.72
√11610.77
√11710.82
√11810.86
√11910.91
√12010.95
√12211.04
√12311.09
√12411.13
√12511.18
√12611.22
√12711.27
√12811.31
√12911.36
√13011.40
√13111.44
√13211.49
√13311.53
√13411.58
√13511.62
√13611.66
√13711.71
√13811.75
√13911.79
√14011.84
√14111.88
√14211.92
√14311.96
√14512.04
√14612.08
√14712.13
√14812.17
√14912.21
√15012.25
√15112.29
√15212.33
√15312.37
√15412.41
√15512.45
√15612.49
√15712.53
√15812.57
√15912.61
√16012.65
√16112.69
√16212.73
√16312.77
√16412.81
√16512.85
√16612.89
√16712.92
√16812.96
√17013.04
√17113.08
√17213.11
√17313.15
√17413.19
√17513.23
√17613.26
√17713.30
√17813.34
√17913.38
√18013.41
√18113.45
√18213.49
√18313.52
√18413.56
√18513.60
√18613.63
√18713.67
√18813.70
√18913.74
√19013.78
√19113.81
√19213.85
√19313.88
√19413.92
√19513.95
√19714.03
√19814.07
√19914.10
√20014.14

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.

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Practice Test

What is the square root of 144?

11

12

13

14

of 10

Which number has a square root of 8?

56

58

64

81

of 10

Find the square root of 121.

10

11

13

12

of 10

What is the square root of 25?

2

3

4

5

of 10

Which number squared equals 36?

5

6

7

8

of 10

What is the square root of 196?

14

15

16

17

of 10

Find the square root of 49.

6

7

8

9

of 10

Which number has a square root of 10?

90

100

110

120

of 10

What is the square root of 81?

8

9

10

11

of 10

Find the square root of 64.

7

8

9

10

of 10

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