You can input a number and find the square root of the number.

## What is Square root?

Square Root definition:

^{2}= 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 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 3 = 1.732

Sqrt of 5 = 2.236

Sqrt of 6 = 2.449

## Table of Square Root (sq rt, sq root)

Square Root of | Square Root is |
---|---|

0 | 0 |

1 | 1 |

2 | 1.414 |

2.25 | 1.5 |

3 | 1.732 |

3.14 | 1.772 |

Pi | 1.772 |

4 | 2 |

5 | 2.236 |

6 | 2.449 |

7 | 2.646 |

8 | 2.828 |

9 | 3 |

10 | 3.162 |

11 | 3.317 |

12 | 3.464 |

13 | 3.606 |

14 | 3.742 |

15 | 3.873 |

16 | 4 |

17 | 4.123 |

18 | 4.243 |

19 | 4.359 |

20 | 4.472 |

21 | 4.583 |

22 | 4.69 |

23 | 4.796 |

24 | 4.899 |

25 | 5 |

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 |

36 | 6 |

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 |

49 | 7 |

50 | 7.071 |

51 | 7.141 |

52 | 7.211 |

53 | 7.28 |

54 | 7.348 |

55 | 7.416 |

56 | 7.483 |

57 | 7.55 |

58 | 7.616 |

59 | 7.681 |

60 | 7.746 |

61 | 7.81 |

62 | 7.874 |

63 | 7.937 |

64 | 8 |

65 | 8.062 |

66 | 8.124 |

67 | 8.185 |

68 | 8.246 |

69 | 8.307 |

70 | 8.367 |

72 | 8.485 |

73 | 8.544 |

74 | 8.602 |

75 | 8.66 |

76 | 8.718 |

77 | 8.775 |

78 | 8.832 |

79 | 8.888 |

80 | 8.944 |

81 | 9 |

82 | 9.055 |

83 | 9.11 |

84 | 9.165 |

85 | 9.22 |

86 | 9.274 |

87 | 9.327 |

88 | 9.381 |

89 | 9.434 |

90 | 9.487 |

91 | 9.539 |

92 | 9.592 |

95 | 9.747 |

96 | 9.798 |

97 | 9.849 |

98 | 9.899 |

99 | 9.95 |

100 | 10 |

105 | 10.247 |

106 | 10.296 |

108 | 10.392 |

109 | 10.44 |

110 | 10.488 |

112 | 10.583 |

113 | 10.63 |

116 | 10.77 |

117 | 10.817 |

119 | 10.909 |

120 | 10.954 |

121 | 11 |

123 | 11.091 |

124 | 11.136 |

125 | 11.18 |

128 | 11.314 |

132 | 11.489 |

135 | 11.619 |

136 | 11.662 |

137 | 11.705 |

140 | 11.832 |

144 | 12 |

145 | 12.042 |

147 | 12.124 |

149 | 12.207 |

150 | 12.247 |

153 | 12.369 |

160 | 12.649 |

162 | 12.728 |

169 | 13 |

175 | 13.229 |

176 | 13.266 |

180 | 13.416 |

181 | 13.454 |

185 | 13.601 |

192 | 13.856 |

193 | 13.892 |

196 | 14 |

200 | 14.142 |

208 | 14.422 |

216 | 14.697 |

221 | 14.866 |

224 | 14.967 |

225 | 15 |

240 | 15.492 |

243 | 15.588 |

244 | 15.62 |

245 | 15.652 |

250 | 15.811 |

256 | 16 |

288 | 16.971 |

289 | 17 |

300 | 17.321 |

306 | 17.493 |

320 | 17.889 |

324 | 18 |

325 | 18.028 |

360 | 18.974 |

361 | 19 |

369 | 19.209 |

400 | 20 |

441 | 21 |

450 | 21.213 |

484 | 22 |

500 | 22.361 |

512 | 22.627 |

529 | 23 |

544 | 23.324 |

576 | 24 |

600 | 24.495 |

625 | 25 |

676 | 26 |

729 | 27 |

784 | 28 |

800 | 28.284 |

841 | 29 |

900 | 30 |

1000 | 31.623 |

1024 | 32 |

1156 | 34 |

1225 | 35 |

1296 | 36 |

1369 | 37 |

1521 | 39 |

1600 | 40 |

1681 | 41 |

2000 | 44.721 |

2025 | 45 |

2304 | 48 |

2500 | 50 |

3600 | 60 |

4096 | 64 |

4225 | 65 |

4761 | 69 |

6400 | 80 |

10000 | 100 |

## What are the different methods to find the Sq root of a number?

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

### 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 1
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 4√2

## Use of Square Roots in real world applications

- 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 has practical application in construction
- Electrical Circuits: Square roots are used in electrical circuit analysis to calculate voltage and current values. It is used in 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.

## 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.

These are square root property:

Numbers 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 square root simplifier.