Square Root Tricks

Knowing square root tricks to find the square of numbers proves to be very helpful when you are solving complex equations which will not take much time for getting solved. Tips and tricks help us to solve mathematical problems easily and quickly. Hence, we have brought here some useful tips to find the square root of a given number even without using a calculator. The concept of squares and the square root is broadly explained in class 8 syllabus.

To find the square root of numbers we have to find out first if the number is a perfect square or not. As we know, there are two conditions for number to know if the number is perfect square:

  • If the number ends with 1, 4, 5, 6, 9, then it is a perfect square
  • If the number ends with 2, 3, 7 and 8, then it is not a perfect square

This one of the basic tip to find square root, which is not enough. Hence we have to learn a few more tricks here.

Also, read:

What is Square Root?

The square root of a number is the value which when multiplied to itself gives the original number. Suppose, 5 when multiplied by 5 results in 25. So we can say, 5 is the square root value of 25. Similarly, 4 is the root value of 16, 6 is the root value 36, 7 is the root value of 49, etc. Since square represents the area of a square which is equal to ‘side x side’, therefore, to square root represents the length of the side of the square. The symbol of the square root is denoted by ‘√’. Hence, square root numbers are represented as √4, √5, √8, √9, etc.

How to Find Square Root?

To find the square root of small numbers like 4, 9, 16, 25, etc. is an easy task. Because we already know from the multiplication table of 1 to 10, the number when multiplied by itself gives the squares, in a two-digit form. But if the number is in three-digit or four-digit, then it is difficult to find the root of these numbers, because we cannot remember the table for higher numbers. Let us find out the trick to determine the root of large numbers.

Example 1:  Suppose we need to find the square root of large numbers such as 4489.

Step 1: The unit digit in this number is 9 which can be a unit digit of its square root number is 3 or 7 because 32 is 9 and 72 is 49.

Step 2: Now let us consider the first two digits that is 44 which comes between the squares of 6 and 7 because 62 < 44< 72

Step 3: We can assume that the ten’s digit of the square root of 4489 is the lowest among the two numbers i.e. 6 and we need to find the unit digit of the square root of the number 4489.

Step 4: Now, we need to find between 63 or 67 which is the square root of 4489.

Step 5: Since the ten’s digit is 6 and the next number is 7, we need to multiply both the numbers like 6 x 7 = 42 and since 42 is less than 44.

Step 6: Square root of 4489 will be the bigger number between 63 and 67 i.e. 67.

Therefore, √4489 = 67

Example 2: Let have a look at another example, the square root of 7056.

Here is the step by step method:

  • Now, consider the unit digit that is 6. Which all numbers have the unit digit 6 on their square roots. That are 4 and 6 because 42 is 16 and 62 is 36.
  • Now let’s consider the first two digits that is 70 which comes between the squares of 8 and 9 because of 82 < 70 <92 .
  • We can assume that the ten’s digit of the square root of the 7056 is the lowest among the two numbers that is 8.
  • Now, we need to find the unit digit of the square root of the number 7056. For that, we need between 84 and 86 which is the square root of 7056.
  • Since the ten’s digit is 8 and the next number is 9, we need to multiply both the numbers like 8 x 9 = 72 and since 72 is bigger than 70.
  • Square root of 7056 will be the lesser number between 84 and 86 that is 84.

Therefore, √7056 = 84

Just like this method, you can get various square roots tricks pdf on the web for finding the square roots of large numbers and with these tricks, you could solve an equation within no time.

Square Root Chart From 1 to 50

You can also memorise the square root table from numbers 1 to 50, to solve problems based on them. Here is the list available:

Number Square Root Value(√)
1 1
2 1.414
3 1.732
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

1 Comment

  1. This was really helpful

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