 # Square Root Calculator

## Find the Square root (sq rt) of any number

HomeMath

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 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

• ### 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 • 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 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) Square Root of Square Root is

0

1

1.414

1.5

1.732

1.772

1.772

2

2.236

2.449

2.646

2.828

3

3.162

3.317

3.464

3.606

3.742

3.873

4

4.123

4.243

4.359

4.472

4.583

4.69

4.796

4.899

5

5.099

5.196

5.292

5.385

5.477

5.568

5.657

5.745

5.831

5.916

6

6.083

6.164

6.245

6.325

6.403

6.481

6.557

6.633

6.708

6.782

6.856

6.928

7

7.071

7.141

7.211

7.28

7.348

7.416

7.483

7.55

7.616

7.681

7.746

7.81

7.874

7.937

8

8.062

8.124

8.185

8.246

8.307

8.367

8.485

8.544

8.602

8.66

8.718

8.775

8.832

8.888

8.944

9

9.055

9.11

9.165

9.22

9.274

9.327

9.381

9.434

9.487

9.539

9.592

9.747

9.798

9.849

9.899

9.95

10

10.247

10.296

10.392

10.44

10.488

10.583

10.63

10.77

10.817

10.909

10.954

11

11.091

11.136

11.18

11.314

11.489

11.619

11.662

11.705

11.832

12

12.042

12.124

12.207

12.247

12.369

12.649

12.728

13

13.229

13.266

13.416

13.454

13.601

13.856

13.892

14

14.142

14.422

14.697

14.866

14.967

15

15.492

15.588

15.62

15.652

15.811

16

16.971

17

17.321

17.493

17.889

18

18.028

18.974

19

19.209

20

21

21.213

22

22.361

22.627

23

23.324

24

24.495

25

26

27

28

28.284

29

30

31.623

32

34

35

36

37

39

40

41

44.721

45

48

50

60

64

65

69

80

100

## Prime Factorization Method • 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 • 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 • 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 • 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 42

## Frequently Asked Questions on Sq Root calculator • 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