Square root of property

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.

Square root of methods

Prime Factorization Method , Repeated Subtraction mehtod , Long Division Method , Estimation Method , Square Root Simplifier

Square Root Calculator

Q: What is Square root?

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 will give a original number.And it is denoted by the symbol √

Q: Square root simplifier

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

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.

Input

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 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.