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Square root from 1 to 100 is a list of square roots of the numbers from 1 to 100. Square root can both possess negative and positive values. The positive values of square roots from 1 to 100 range from 1 to 10.
- The square root of a number is the factor of a number that, when multiplied by itself, gives the original number.
- This means it is the value at which one number is divided by another number.
- It is used in the field of mathematics to solve various types of problems.
- The concept of square root is used in probability, physics, architecture, statistics and engineering.
- It is denoted by the symbol √.
Square Root chart 1 to 100:
- In case of radical form: √x
- In case of exponential form: (x)½
Here, x is any number between 1 to 100.
Key Terms: Square root from 1 to 100, Square Root, Radicant, Radical Symbol, Prime Factorisation, Long Division, Repeated Subtraction, Exponential Form, Number, Estimation Method
Square Root
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The square root of a number is just antagonistic to the squaring of a number. The symbol of the square root is √. The symbol is known as the Radical Symbol, and the number given below is known as Radicant.
- The one thing you have to do is find out which given number is the square of the number provided.
- Let 'x' be an integer, and then the square root of that number is √x = y (y × y = x).
- It can be read as 'square root of x is equal to y'.
- Here, the number x is known as the "Radicant".
- Numbers like 1, 4, 9, 16, 25, 36, 49, 64, 81, and 100 belong to the category of perfect squares.
- The remaining numbers are non-perfect squares, which means their square root is irrational.
Example of Square RootExample: Thus, √49 = 7 Here, 49 is the square of 7. |
Square Root of a Number Example
Read More:
| Chapter Related Concepts | ||
|---|---|---|
| Cosine Rule | Arithmetic | face value and place value |
| Fraction | Degree of polynomial | Number Systems |
How to calculate Square Root from 1 to 100?
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The square root of a number can be found in various ways which are as follows:
Prime Factorisation
Square root of a perfect square number can be easily found by prime factorisation. It is demonstrated below in the table.
| Number | Prime Factorisation | Square Root |
|---|---|---|
| 256 | 2×2×2×2×2×2×3×3 | 2×2×2×3 = 24 |
| 169 | 13×13 | 13 |
| 144 | 2×2×2×2×3×3 | 2×2×3= 12 |
| 81 | 3×3×3×3 | 3×3= 9 |
| 25 | 5×5 | 5 |
Repeated Subtraction
Repeated subtraction is also one of the ways in which the square root of a perfect square number can be found out. Here the number given is subtracted by consecutive odd numbers until we get zero.
- The below example demonstrates it.
Example of Repeated SubtractionExample 1: √36 36-1 = 35 35-3 = 32 32-5 = 27 27-7 = 20 20-9 = 11 11-11 = 0 Here the subtraction has to be done in 6 steps. Therefore the square root of 36 is 6. Example 2: √81 81-1= 80 80-3= 77 77-5= 72 72-7= 75 65-9= 56 56-11= 45 45-13= 32 32-15= 17 17-17= 0 Here the subtraction has to be done in 9 steps. Therefore the square root of 81 is 9. |
Square Root by Long Division Method
Finding the square root of an imperfect square number is considerably difficult. Although, it can be found out by an easy method namely the long division method.
Example of Square Root by Long Division MethodExample: An example of the same is given below.
Square Root by Long Division Method
|
Read Also:
Square Root by Estimation
In this method, the square root of a number can be found by taking the approximating value of the perfect square number which is before and after the given number.
- This method is employed in finding square roots of imperfect squares.
Example by Square Root by EstimationExample: For example, if we want to calculate the square root of the number 5, we can think about the perfect square before and after 5.
Hence, ⇒ 2.2 × 2.2 = 4.4 ⇒ 2.3 × 2.3 = 5.29 As 4.4 is closer to 5. We can consider 2.2 as the approximate square root of the number 5. |
List of Square root from 1 to 100
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The following table consists of square 1 to 100:
| Square Root 1 to 100 | ||
|---|---|---|
| Numbers upto 100 (N) | Squares Upto 100 (N2) | Square root (√N) |
| 1 | 1 | 1.000 |
| 2 | 4 | 1.414 |
| 3 | 9 | 1.732 |
| 4 | 16 | 2.000 |
| 5 | 25 | 2.236 |
| 6 | 36 | 2.449 |
| 7 | 49 | 2.646 |
| 8 | 64 | 2.828 |
| 9 | 81 | 3.000 |
| 10 | 100 | 3.162 |
| 11 | 121 | 3.317 |
| 12 | 144 | 3.464 |
| 13 | 169 | 3.606 |
| 14 | 196 | 3.742 |
| 15 | 225 | 3.873 |
| 16 | 256 | 4.000 |
| 17 | 289 | 4.123 |
| 18 | 324 | 4.243 |
| 19 | 361 | 4.359 |
| 20 | 400 | 4.472 |
| 21 | 441 | 4.583 |
| 22 | 484 | 4.690 |
| 23 | 529 | 4.796 |
| 24 | 576 | 4.899 |
| 25 | 625 | 5.000 |
| 26 | 676 | 5.099 |
| 27 | 729 | 5.196 |
| 28 | 784 | 5.292 |
| 29 | 841 | 5.385 |
| 30 | 900 | 5.477 |
| 31 | 961 | 5.568 |
| 32 | 1024 | 5.657 |
| 33 | 1089 | 5.745 |
| 34 | 1156 | 5.831 |
| 35 | 1225 | 5.916 |
| 36 | 1296 | 6.000 |
| 37 | 1369 | 6.083 |
| 38 | 1444 | 6.164 |
| 39 | 1521 | 6.245 |
| 40 | 1600 | 6.325 |
| 41 | 1681 | 6.403 |
| 42 | 1764 | 6.481 |
| 43 | 1849 | 6.557 |
| 44 | 1936 | 6.633 |
| 45 | 2025 | 6.708 |
| 46 | 2116 | 6.782 |
| 47 | 2209 | 6.856 |
| 48 | 2304 | 6.928 |
| 49 | 2401 | 7.000 |
| 50 | 2500 | 7.071 |
| 51 | 2601 | 7.141 |
| 52 | 2704 | 7.211 |
| 53 | 2809 | 7.280 |
| 54 | 2916 | 7.348 |
| 55 | 3025 | 7.416 |
| 56 | 3136 | 7.483 |
| 57 | 3249 | 7.550 |
| 58 | 3364 | 7.616 |
| 59 | 3481 | 7.681 |
| 60 | 3600 | 7.746 |
| 61 | 3721 | 7.810 |
| 62 | 3844 | 7.874 |
| 63 | 3969 | 7.937 |
| 64 | 4096 | 8.000 |
| 65 | 4225 | 8.062 |
| 66 | 4356 | 8.124 |
| 67 | 4489 | 8.185 |
| 68 | 4624 | 8.246 |
| 69 | 4761 | 8.307 |
| 70 | 4900 | 8.367 |
| 71 | 5041 | 8.426 |
| 72 | 5184 | 8.485 |
| 73 | 5329 | 8.544 |
| 74 | 5476 | 8.602 |
| 75 | 5625 | 8.660 |
| 76 | 5776 | 8.718 |
| 77 | 5929 | 8.775 |
| 78 | 6084 | 8.832 |
| 79 | 6241 | 8.888 |
| 80 | 6400 | 8.944 |
| 81 | 6561 | 9.000 |
| 82 | 6724 | 9.055 |
| 83 | 6889 | 9.110 |
| 84 | 7056 | 9.165 |
| 85 | 7225 | 9.220 |
| 86 | 7396 | 9.274 |
| 87 | 7569 | 9.327 |
| 88 | 7744 | 9.381 |
| 89 | 7921 | 9.434 |
| 90 | 8100 | 9.487 |
| 91 | 8281 | 9.539 |
| 92 | 8464 | 9.592 |
| 93 | 8649 | 9.644 |
| 94 | 8836 | 9.695 |
| 95 | 9025 | 9.747 |
| 96 | 9216 | 9.798 |
| 97 | 9409 | 9.849 |
| 98 | 9604 | 9.899 |
| 99 | 9801 | 9.950 |
| 100 | 10000 | 10.000 |
Square Root 1 to 100 for Non-Perfect Squares
The square root table 1 to 100 for non-perfect squares is tabulated below:
| Square Root 1 to 100 (Non-Perfect Squares) | ||||
|---|---|---|---|---|
| √2 = 1.414 | √3 = 1.732 | √5 = 2.236 | √6 = 2.449 | √7 = 2.646 |
| √8 = 2.828 | √10 = 3.162 | √11 = 3.317 | √12 = 3.464 | √13 = 3.606 |
| √14 = 3.742 | √15 = 3.873 | √17 = 4.123 | √18 = 4.243 | √19 = 4.359 |
| √20 = 4.472 | √21 = 4.583 | √22 = 4.690 | √23 = 4.796 | √24 = 4.899 |
| √26 = 5.099 | √27 = 5.196 | √28 = 5.292 | √29 = 5.385 | √30 = 5.477 |
| √31 = 5.568 | √32 = 5.657 | √33 = 5.745 | √34 = 5.831 | √35 = 5.916 |
| √37 = 6.083 | √38 = 6.164 | √39 = 6.245 | √40 = 6.325 | √41 = 6.403 |
| √42 = 6.481 | √43 = 6.557 | √44 = 6.633 | √45 = 6.708 | √46 = 6.782 |
| √47 = 6.856 | √48 = 6.928 | √50 = 7.071 | √51 = 7.141 | √52 = 7.211 |
| √53 = 7.280 | √54 = 7.348 | √55 = 7.416 | √56 = 7.483 | √57 = 7.550 |
| √58 = 7.616 | √59 = 7.681 | √60 = 7.746 | √61 = 7.810 | √62 = 7.874 |
| √63 = 7.937 | √65 = 8.062 | √66 = 8.124 | √67 = 8.185 | √68 = 8.246 |
| √69 = 8.307 | √70 = 8.367 | √71 = 8.426 | √72 = 8.485 | √73 = 8.544 |
| √74 = 8.602 | √75 = 8.660 | √76 = 8.718 | √77 = 8.775 | √78 = 8.832 |
| √79 = 8.888 | √80 = 8.944 | √82 = 9.055 | √83 = 9.110 | √84 = 9.165 |
| √85 = 9.220 | √86 = 9.274 | √87 = 9.327 | √88 = 9.381 | √89 = 9.434 |
| √90 = 9.487 | √91 = 9.539 | √92 = 9.592 | √93 = 9.644 | √94 = 9.695 |
| √95 = 9.747 | √96 = 9.798 | √97 = 9.849 | √98 = 9.899 | √99 = 9.950 |
Perfect Squares from 1 to 100
Perfect Square Numbers from 1 To 100 with their factors (product of integers) are listed below
| Perfect square numbers from 1 to 100 | ||||
|---|---|---|---|---|
| 1 | = | 1 × 1 | = | 12 |
| 4 | = | 2 × 2 | = | 22 |
| 9 | = | 3 × 3 | = | 32 |
| 16 | = | 4 × 4 | = | 42 |
| 25 | = | 5 × 5 | = | 52 |
| 36 | = | 6 × 6 | = | 62 |
| 49 | = | 7 × 7 | = | 72 |
| 64 | = | 8 × 8 | = | 82 |
| 81 | = | 9 × 9 | = | 92 |
| 100 | = | 10 × 10 | = | 102 |
Things to Remember
- Square Root 1 to 100 can be expressed as the factor of a number that, when multiplied by itself, gives the original number.
- It can be found for only two types of numbers, namely perfect square and imperfect square.
- Perfect squares are those in which the number can be found easily by identifying the same factor in that number.
- There are four different ways to find the square root of a number.
- Prime Factorisation, Repeated Subtraction, Long Division Method, and Estimation Method are those methods.
Read Also:
| Chapter 6 Mathematics Related Concept | ||
|---|---|---|
| Real Numbers | Root Mean Square Formula | Sum of Squares |
| Estimating Square Roots | Finding Square root | Prime Numbers |
Sample Questions
Ques. Calculate the value of y; if y = 3√81. (1 mark)
Ans. y = 3 √81
√81 = 9
Therefore,
⇒ 3√81 = 3×9 = 27
Ques. Determine the value of 7√49. (1 mark)
Ans. √49= 7
Therefore,
⇒ 7√49 = 7×7 = 49
Ques. Find the value of x; if x√36 = 180. (2 marks)
Ans. x√36 = 180
√36 = 6
Therefore x√36
⇒ x × 6 = 180
⇒ 6x = 180
⇒ x = 180/6 = 30
Ques. Find √50. (2 marks)
Ans. As 50 is not a perfect square; we cannot calculate its value through prime factorisation or repeated subtraction. Let us see if there is any alternative method.
√50 = √2×25
= √2 × √25
= √2 × 5
= 5√2
As the value of √2 = 1.44
5√2 = 5 × 1.44 = 7.2
This can be found out via estimation methods as well.
Ques. Find the square root of the decimal number 1056.25. (2 marks)
Ans. For 1056.25
That is, √1056.25 = 32.5
Ques. Find the square root of the decimal number 10020.01. (2 marks)
Ans. Here, for 10020.01
That is √10020.01 = 100.1
Ques. What is the square root of the following numbers. (3 marks)
(a) 76
(b) 26
(c) 18
Ans. The square root of the following numbers are:
- 76 = 8.718
- 26 = 5.099
- 18 = 4.123
Ques. Find out the square root of 100 via repeated subtraction. (3 marks)
Ans. The square root of 100 via repeated subtraction:
100 - 1 = 99
99 - 3 = 96
96 - 5 = 91
91 - 7 = 84
84 - 9 = 75
75 - 11 = 64
64 - 13 = 51
51 - 15 = 36
36 - 17 = 19
19-19 = 0
As the steps involved in this was 10 and the final answer is zero.
Thus, the square root of 100 is 10.
Ques. Check whether the following numbers are perfect squares using the prime factorisation method: (3 marks)
(a) 625
(b) 768
Ans. By prime factorisation method:
- 625
√625=
5|625
5| 125
5| 25
5| 5
| 1
√625= 5×5×5×5
= (5×5) (5×5)
As the obtained numbers become pairs 625 is a perfect square.
5×5= 25 is the square root of 625
- √768 =
2| 768
2| 384
2| 192
2| 96
2|48
2| 24
2| 12
2| 6
3| 3
| 1
√768 = 2×2×2×2×2×2×2×2×3
= (2×2) (2×2) (2×2) (2×2) 3
As 3 is not in pairs ; 768 is not a perfect square.
Ques. Complete the following (4 marks)
(a) The perfect squares between 40 and 100 are ______.
(b) ____ is the square root of 49/144
(c) (-5)2 is 25. What is the square root of 25?
(d) Find the value of √45
Ans. Here,
- The perfect squares between 40 and 100 are 49, 64, and 81
- 7/12 is the square root of 49/144
- (-5)2 = 25 Then √25 = +5 and -5
- √45= √9×5
= √9 × √5
= 3 × √5
(value of √5= 2.36 approximately)
3 × 2.36 = 7.08
Ques. Which is the smallest whole number by which 768 should be multiplied in order to get a perfect square number. Determine the square root of the number thus obtained. (5 marks)
Ans. Here,
- √768 =
2| 768
2| 384
2| 192
2| 96
2|48
2| 24
2| 12
2| 6
3| 3
| 1
√768 = 2×2×2×2×2×2×2×2×3
= (2×2) (2×2) (2×2) (2×2) 3
As 3 is not a pair, the above number is not a perfect square. So as to get a perfect square root 3 needs to be in pairs and another 3 has to be multiplied.
Hence it will change into
(2×2) (2×2) (2×2) (2×2) (3×3)
Therefore the perfect square number thus we get is 768 × 3 = 2304
Thus, after obtaining √2304, the square root can be expressed as:
2304 = 2 × 2 × 2 × 2 × 2 × 2 × 2 × 2 × 3 × 3
= (2 × 2) (2 × 2) (2 × 2) (2 × 2) (3 × 3)
= 2 × 2 × 2 × 2 × 3
= 48
Ques. A square metal sheet has an area of 900 sq. inches. Find the length of the side of the metal sheet. (2 marks)
Ans. Let ‘a’ be the length of the side of the metal sheet
Area of the square metal sheet = 40 in2 = a2
a2 = 900
a = √900 = 30 in
Ques. If a circular tabletop has an area of 49π sq. inches. Find the radius of the tabletop in inches. (2 marks)
Ans. Area of circular tabletop = 49π = πr2
49 = r2. Hence, radius = √7
Ques. Find the value of √81 using the prime factorization method. (2 marks)
Ans. As it is known that,
- Prime factorization of 81 is 9 × 9
- Pairing Prime Factors: 9
- Thus, the value of √81 = 9
Ques. A circular pond has an area of 176 m2. Find the radius of the pond. (2 marks)
Ans. Consider r be the radius of the pond
- Area of Pond = 176 m2
- We know that,
- Area of Pond = πr2
- πr2 = 176
- 22/7r2 = 176
- r2 = 8×7
- r = √56
Ques. A square park has an area of 169 m2. Find the length of the park. (2 marks)
Ans. Consider z be the length of the Park.
- Area of Square Park = 169 m2
- Area of Square = z2
- z2 = 169
- z = √(169)
- z=13
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