 # 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

### Video Lesson Test your knowledge on Square Root Numbers