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Square Root Calculator

Find the Square root (sq rt) of any number

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Square Root

You can input a number and find the square root of the number.
Square root of 4 is 2

What is Square root?

square-root icon

  • Square Root definition:

A number (x) is said to be a square root of (y) number if x2 = y.
(i.e)when we multiply the square root of a number by itself, it will give the original number. It is denoted by the symbol √

  • The short forms are sq root, sqrt and the symbol used for sq rt is √

  • Square Root of first 5 perfect square numbers.

Square root of 1 = 1
Square root of 4 = 2
Square root of 9 = 3
Square root of 16 = 4
Square root of 25 = 5

  • Square Root of some common numbers.

Sqrt of 2 = 1.414
Sqrt of 3 = 1.732
Sqrt of 5 = 2.236
Sqrt of 6 = 2.449

  • Methods to find Square Root of number.

  • Prime Factorization Method
  • Repeated Subtraction Method
  • Long Division Method
  • Estimation Method
  • Square Root Simplifier

Interesting facts about Square Root

Interesting Icon
  • The first known square root calculator was invented by the Greek mathematician Heron of Alexandria in the 1st century AD. His method, known as Heron's method.
  • The square root of a negative number is an imaginary number.
  • The square root of a fraction is the square root of the numerator divided by the square root of the denominator.
  • The square root of a product is the product of the square roots of the factors.
  • The square root of a quotient is the quotient of the square root of the dividend divided by the square root of the divisor.
  • The square root of a prime number is irrational, meaning it cannot be expressed as a finite decimal or fraction.
  • The square root of a perfect square is a rational number, meaning it can be expressed as a finite decimal or fraction.
  • The square root of a number can be approximated using various methods, such as the Babylonian method or Newton's method.
  • Square root calculators have a wide range of applications outside of mathematics, including physics, engineering, finance, and computer science.
  • Calculating Distance: The Pythagorean theorem, a fundamental concept in geometry, uses square roots to determine the length of the hypotenuse in a right-angled triangle. This is crucial for various applications, such as carpentry, construction, and surveying.
  • Electrical Circuits: Square roots are used in electrical circuit analysis to calculate voltage and current values. This is essential for designing and maintaining efficient electrical systems.
  • Finance and Investments: Square roots are employed in finance to calculate the annualized rate of return on investments and to assess the risk associated with different financial instruments.
  • Physics and Engineering: Square roots are used in various physics and engineering applications, including calculating force, velocity, and energy. They are also used in fluid dynamics, optics, and thermodynamics.
  • Probability and Statistics: Square roots are used in probability and statistics to calculate standard deviation, a measure of the spread of data. This is important for understanding the variability of data sets.
  • Computer Graphics and Animation: Square roots are used in computer graphics and animation to calculate distances between objects and to generate realistic lighting effects.
  • Everyday Calculations: Square roots are used in everyday calculations, such as determining the diagonal length of a rectangle or calculating the area of a circle.

Square Root Computation Methods

Computation Icon
Newton's method and the Babylonian method are essentially the same algorithm except for the initial guess number.
Newton's Method to find Square Root
Newton's method is an iterative method for finding the roots of equations. It is based on the idea of linearizing the equation at a point and then using the slope of the tangent line to estimate the root.
To find the square root of a number N using Newton's method, follow these steps:
  • Start with an initial guess for the square root. A good guess is often half of the number.
  • Calculate the next guess using the formula: guess = (guess + N / guess) / 2
  • Repeat step 2 until the desired accuracy is reached.
Babylonian Method to find Square Root
The Babylonian method is another iterative method for finding square roots. It is thought to have been used by the Babylonians as early as 1800 BC.
To find the square root of a number N using the Babylonian method, follow these steps:
  • Start with an initial guess for the square root. A good guess is any positive number.
  • Calculate the next guess using the formula: guess = (guess + N / guess) / 2
  • Repeat step 2 until the desired accuracy is reached.
Other Methods
There are a number of other methods for finding square roots, including:
  • Long division: This method is similar to the method for long division of integers.
  • Logarithms: The square root of a number can be found by taking the logarithm of the number and then dividing by 2.
  • Tables of square roots: Tables of square roots were once used to find square roots, but they have been largely superseded by calculators and computers.
Comparison of Methods
Newton's method and the Babylonian method are both iterative methods, which means that they require multiple guesses to find the solution. Newton's method is generally faster than the Babylonian method, but it can be more sensitive to the initial guess.
Long division is a more manual method, but it can be useful for finding square roots to a high degree of precision.
Logarithms and tables of square roots are no longer commonly used, but they are still of historical interest.

Table of Square Root (sq rt, sq root)

Conversion Table Icon
Square Root of Square Root is

Square root of 0 (sqrt of 0)

0

Square root of 1 (sqrt of 1)

1

Square root of 2 (sqrt of 2)

1.414

Square root of 2.25 (sqrt of 2.25)

1.5

Square root of 3 (sqrt of 3)

1.732

Square root of 3.14 (sqrt of 3.14)

1.772

Square root of Pi (sqrt of Pi)

1.772

Square root of 4 (sqrt of 4)

2

Square root of 5 (sqrt of 5)

2.236

Square root of 6 (sqrt of 6)

2.449

Square root of 7 (sqrt of 7)

2.646

Square root of 8 (sqrt of 8)

2.828

Square root of 9 (sqrt of 9)

3

Square root of 10 (sqrt of 10)

3.162

Square root of 11 (sqrt of 11)

3.317

Square root of 12 (sqrt of 12)

3.464

Square root of 13 (sqrt of 13)

3.606

Square root of 14 (sqrt of 14)

3.742

Square root of 15 (sqrt of 15)

3.873

Square root of 16 (sqrt of 16)

4

Square root of 17 (sqrt of 17)

4.123

Square root of 18 (sqrt of 18)

4.243

Square root of 19 (sqrt of 19)

4.359

Square root of 20 (sqrt of 20)

4.472

Square root of 21 (sqrt of 21)

4.583

Square root of 22 (sqrt of 22)

4.69

Square root of 23 (sqrt of 23)

4.796

Square root of 24 (sqrt of 24)

4.899

Square root of 25 (sqrt of 25)

5

Square root of 26 (sqrt of 26)

5.099

Square root of 27 (sqrt of 27)

5.196

Square root of 28 (sqrt of 28)

5.292

Square root of 29 (sqrt of 29)

5.385

Square root of 30 (sqrt of 30)

5.477

Square root of 31 (sqrt of 31)

5.568

Square root of 32 (sqrt of 32)

5.657

Square root of 33 (sqrt of 33)

5.745

Square root of 34 (sqrt of 34)

5.831

Square root of 35 (sqrt of 35)

5.916

Square root of 36 (sqrt of 36)

6

Square root of 37 (sqrt of 37)

6.083

Square root of 38 (sqrt of 38)

6.164

Square root of 39 (sqrt of 39)

6.245

Square root of 40 (sqrt of 40)

6.325

Square root of 41 (sqrt of 41)

6.403

Square root of 42 (sqrt of 42)

6.481

Square root of 43 (sqrt of 43)

6.557

Square root of 44 (sqrt of 44)

6.633

Square root of 45 (sqrt of 45)

6.708

Square root of 46 (sqrt of 46)

6.782

Square root of 47 (sqrt of 47)

6.856

Square root of 48 (sqrt of 48)

6.928

Square root of 49 (sqrt of 49)

7

Square root of 50 (sqrt of 50)

7.071

Square root of 51 (sqrt of 51)

7.141

Square root of 52 (sqrt of 52)

7.211

Square root of 53 (sqrt of 53)

7.28

Square root of 54 (sqrt of 54)

7.348

Square root of 55 (sqrt of 55)

7.416

Square root of 56 (sqrt of 56)

7.483

Square root of 57 (sqrt of 57)

7.55

Square root of 58 (sqrt of 58)

7.616

Square root of 59 (sqrt of 59)

7.681

Square root of 60 (sqrt of 60)

7.746

Square root of 61 (sqrt of 61)

7.81

Square root of 62 (sqrt of 62)

7.874

Square root of 63 (sqrt of 63)

7.937

Square root of 64 (sqrt of 64)

8

Square root of 65 (sqrt of 65)

8.062

Square root of 66 (sqrt of 66)

8.124

Square root of 67 (sqrt of 67)

8.185

Square root of 68 (sqrt of 68)

8.246

Square root of 69 (sqrt of 69)

8.307

Square root of 70 (sqrt of 70)

8.367

Square root of 72 (sqrt of 72)

8.485

Square root of 73 (sqrt of 73)

8.544

Square root of 74 (sqrt of 74)

8.602

Square root of 75 (sqrt of 75)

8.66

Square root of 76 (sqrt of 76)

8.718

Square root of 77 (sqrt of 77)

8.775

Square root of 78 (sqrt of 78)

8.832

Square root of 79 (sqrt of 79)

8.888

Square root of 80 (sqrt of 80)

8.944

Square root of 81 (sqrt of 81)

9

Square root of 82 (sqrt of 82)

9.055

Square root of 83 (sqrt of 83)

9.11

Square root of 84 (sqrt of 84)

9.165

Square root of 85 (sqrt of 85)

9.22

Square root of 86 (sqrt of 86)

9.274

Square root of 87 (sqrt of 87)

9.327

Square root of 88 (sqrt of 88)

9.381

Square root of 89 (sqrt of 89)

9.434

Square root of 90 (sqrt of 90)

9.487

Square root of 91 (sqrt of 91)

9.539

Square root of 92 (sqrt of 92)

9.592

Square root of 95 (sqrt of 95)

9.747

Square root of 96 (sqrt of 96)

9.798

Square root of 97 (sqrt of 97)

9.849

Square root of 98 (sqrt of 98)

9.899

Square root of 99 (sqrt of 99)

9.95

Square root of 100 (sqrt of 100)

10

Square root of 105 (sqrt of 105)

10.247

Square root of 106 (sqrt of 106)

10.296

Square root of 108 (sqrt of 108)

10.392

Square root of 109 (sqrt of 109)

10.44

Square root of 110 (sqrt of 110)

10.488

Square root of 112 (sqrt of 112)

10.583

Square root of 113 (sqrt of 113)

10.63

Square root of 116 (sqrt of 116)

10.77

Square root of 117 (sqrt of 117)

10.817

Square root of 119 (sqrt of 119)

10.909

Square root of 120 (sqrt of 120)

10.954

Square root of 121 (sqrt of 121)

11

Square root of 123 (sqrt of 123)

11.091

Square root of 124 (sqrt of 124)

11.136

Square root of 125 (sqrt of 125)

11.18

Square root of 128 (sqrt of 128)

11.314

Square root of 132 (sqrt of 132)

11.489

Square root of 135 (sqrt of 135)

11.619

Square root of 136 (sqrt of 136)

11.662

Square root of 137 (sqrt of 137)

11.705

Square root of 140 (sqrt of 140)

11.832

Square root of 144 (sqrt of 144)

12

Square root of 145 (sqrt of 145)

12.042

Square root of 147 (sqrt of 147)

12.124

Square root of 149 (sqrt of 149)

12.207

Square root of 150 (sqrt of 150)

12.247

Square root of 153 (sqrt of 153)

12.369

Square root of 160 (sqrt of 160)

12.649

Square root of 162 (sqrt of 162)

12.728

Square root of 169 (sqrt of 169)

13

Square root of 175 (sqrt of 175)

13.229

Square root of 176 (sqrt of 176)

13.266

Square root of 180 (sqrt of 180)

13.416

Square root of 181 (sqrt of 181)

13.454

Square root of 185 (sqrt of 185)

13.601

Square root of 192 (sqrt of 192)

13.856

Square root of 193 (sqrt of 193)

13.892

Square root of 196 (sqrt of 196)

14

Square root of 200 (sqrt of 200)

14.142

Square root of 208 (sqrt of 208)

14.422

Square root of 216 (sqrt of 216)

14.697

Square root of 221 (sqrt of 221)

14.866

Square root of 224 (sqrt of 224)

14.967

Square root of 225 (sqrt of 225)

15

Square root of 240 (sqrt of 240)

15.492

Square root of 243 (sqrt of 243)

15.588

Square root of 244 (sqrt of 244)

15.62

Square root of 245 (sqrt of 245)

15.652

Square root of 250 (sqrt of 250)

15.811

Square root of 256 (sqrt of 256)

16

Square root of 288 (sqrt of 288)

16.971

Square root of 289 (sqrt of 289)

17

Square root of 300 (sqrt of 300)

17.321

Square root of 306 (sqrt of 306)

17.493

Square root of 320 (sqrt of 320)

17.889

Square root of 324 (sqrt of 324)

18

Square root of 325 (sqrt of 325)

18.028

Square root of 360 (sqrt of 360)

18.974

Square root of 361 (sqrt of 361)

19

Square root of 369 (sqrt of 369)

19.209

Square root of 400 (sqrt of 400)

20

Square root of 441 (sqrt of 441)

21

Square root of 450 (sqrt of 450)

21.213

Square root of 484 (sqrt of 484)

22

Square root of 500 (sqrt of 500)

22.361

Square root of 512 (sqrt of 512)

22.627

Square root of 529 (sqrt of 529)

23

Square root of 544 (sqrt of 544)

23.324

Square root of 576 (sqrt of 576)

24

Square root of 600 (sqrt of 600)

24.495

Square root of 625 (sqrt of 625)

25

Square root of 676 (sqrt of 676)

26

Square root of 729 (sqrt of 729)

27

Square root of 784 (sqrt of 784)

28

Square root of 800 (sqrt of 800)

28.284

Square root of 841 (sqrt of 841)

29

Square root of 900 (sqrt of 900)

30

Square root of 1000 (sqrt of 1000)

31.623

Square root of 1024 (sqrt of 1024)

32

Square root of 1156 (sqrt of 1156)

34

Square root of 1225 (sqrt of 1225)

35

Square root of 1296 (sqrt of 1296)

36

Square root of 1369 (sqrt of 1369)

37

Square root of 1521 (sqrt of 1521)

39

Square root of 1600 (sqrt of 1600)

40

Square root of 1681 (sqrt of 1681)

41

Square root of 2000 (sqrt of 2000)

44.721

Square root of 2025 (sqrt of 2025)

45

Square root of 2304 (sqrt of 2304)

48

Square root of 2500 (sqrt of 2500)

50

Square root of 3600 (sqrt of 3600)

60

Square root of 4096 (sqrt of 4096)

64

Square root of 4225 (sqrt of 4225)

65

Square root of 4761 (sqrt of 4761)

69

Square root of 6400 (sqrt of 6400)

80

Square root of 10000 (sqrt of 10000)

100

Prime Factorization Method

User Guide icon
  • Step 1:

    Divide the given number by its prime factor.

  • Step 2

    Make pairs of similar factors

  • Step 3:

    From each pair take one factor and multiply them this will give you the square root of the given number.

  • Example: Lets find the square root of 100.

    Prime Factorization of 100 = 2 x 2 x 5 x 5;
    Take 2 and 5 from the pairs.Product of 2 and 5 is the square root of 100.
    so 10 is the square root of 100.

Repeated Subtraction Method

User Guide icon
  • Step 1:

    This is used only if the number is perfect square.Subtract the consecutive odd numbers from the given number.

  • Step 2:

    Subtract till you get diference as 0.

  • Step 3:

    Number of times we subtract will be the square root of the given number.

  • Example:Square root of 36.
  • 36 - 1 = 35
  • 35 - 3 = 31
  • 31 - 5 = 29
  • 29 - 7 = 22
  • 22 - 9 = 11
  • 11 - 11 = 0

Since we subtracted for 6 times ,So 6 is the square root of 36.

Long DIvision Method

User Guide icon
  • Step 2

    Separate the given number from right to left with two digit in a seperation.

  • Step 2

    Now think of a perfect square number that is closest to the first pair in the left side and divide the given number with that number.

  • Step 3:

    Bring down the remainder along with the next pair, and multiply the previous quotient by 2 and bring it down.

  • Step 4:

    Repeat step 2 and step 3 untill you get the remainder as zero.If necessary we can add decimal to get zero at the end.

  • Long division Flow

Square Root Simplifier Method

User Guide icon
  • Step 1:

    Write the prime factorization of the given number inside the radical.

  • Step 2:

    Pair each number and take them out from the square root.

  • Step 3:

    Leave the number insode the root that dont have pair.Multiply the number that are taken from the root and the number with the root.

  • Example:Square root of 32.

    Prime factorization of √32 is √2 x 2 x 2 x 2 x 2 = 2 x 2 √2

    Square root of 32 is 4√2

Frequently Asked Questions on Sq Root calculator

FAQ icon

  • A number (x) is said to be a square root of (y) number if x^2 = y.

  • For example:Square root of 25 is 5.

  • Number with 2, 3, 7 or 8 at unit’s place is never a perfect square. Squares of even numbers are always even numbers and square of odd numbers are always odd.

  • Taking out all the perfect squares from the radicand is simplifier square root.

  • Square root of 9 is 3.

  • Square root of 2 is 1.414.

  • Square root of 8 is 2.828

  • Square root of 3 is 1.732.

  • Square root of 5 is 2.2360.

  • Square root of 64 is 8.

  • 1000 square root is 31.622.

  • Square root of 10 is 3.162.

  • Square root of 169 is 13.

  • Square root of 12 is 3.4641.

  • Square root of 20 is 4.4721.

  • Square root of 4761 is 69.

  • Square root of 6 is 2.44949