Square Root Numbers

The square root numbers are the list of those numbers which when multiplied by themselves produces the original numbers. The symbol used to represent the square root is a radical sign, i.e. ‘√’. The number present under the radical symbol is called ‘radicand’. This concept is one of the important concepts for Class 9 students.

To learn about square roots, we should first learn about squares of numbers. Then it will be easy for us to find the square roots of the numbers. When we multiply a number to itself, then it is said to be square of that number. Suppose ‘a’ is a number and is multiplied by itself, then it is said to be a squared. For example, 2 x 2 = 22 = 4. Now, if we find the square root of 4 then we get the original number, i.e. 2. Since, 4 is a perfect square, therefore it can be easily factorised by the prime factorisation method to evaluate the square root. See some more examples below:

  • 3 squared = 32 = 9 & √9 = 3
  • 7 squared = 72 = 49 & √49 = 7
  • 11 squared = 112 = 121 & √121 = 11
  • 12 squared = 122 = 144 & √144 = 12

Finding the square root of numbers which are very large or which are imperfect squares, could be a difficult task. Hence, to find the square root of such numbers in an easy and the fastest way, we use the long division method.

Square Root Numbers List

Here is the list of the square of numbers and their square roots. The table given below can be memorised by students easily so that they can solve questions based on these square root values.

Number (n) Square (n2) Square root (√n)
1 1 1
2 4 1.4142
3 9 1.7321
4 16 2
5 25 2.2361
6 36 2.4495
7 49 2.6458
8 64 2.8284
9 81 3
10 100 3.1623
11 121 3.3166
12 144 3.4641
13 169 3.6056
14 196 3.7417
15 225 3.8730
16 256 4
17 289 4.1231
18 324 4.2426
19 361 4.3589
20 400 4.4721
21 441 4.5826
22 484 4.6904
23 529 4.7958
24 576 4.8990
25 625 5
26 676 5.0990
27 729 5.1962
28 784 5.2915
29 841 5.3852
30 900 5.4772
31 961 5.5678
32 1024 5.6569
33 1089 5.7446
34 1156 5.8310
35 1225 5.9161
36 1296 6
37 1369 6.0828
38 1444 6.1644
39 1521 6.2450
40 1600 6.3246
41 1681 6.4031
42 1764 6.4807
43 1849 6.5574
44 1936 6.6332
45 2025 6.7082
46 2116 6.7823
47 2209 6.8557
48 2304 6.9282
49 2401 7
50 2500 7.0711

Square Root Problems

Based on the table above we can solve the questions given here.

  1. Solve √50 + √2 + √9
  2. Multiply: √3 and √7
  3. Divide: √49 by 7
  4. Simplify: (√8 x √9) + √89
  5. Simplify: 2√4+3√9+5√25

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