# 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
• 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

## 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 42

## 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.