Squaring a number is the inverse procedure of square rooting it. The square root of a number is the number that needs to be multiplied by itself to get the original number, whereas the square of a number is the number that needs to be multiplied by itself to get the original number. Square root is a complex operation. Hence, it can be a time-consuming operation to obtain the square roots of a number. There are some tricks that can be used to determine the square root of a number faster. In this maths article, we will learn about the different tricks to find the square root of a number, square root tricks for 3 digit,4 digit, and 5 digit numbers, and solve some problems based on the square root tricks.

What is Square Root 

The square root of a number is the value that, when multiplied by itself, gives the original number. For example, the square root of 625 is 25 because 25 × 25 = 625. We use the symbol √ to show the square root, like √9 = 3. If a number is a perfect square, its square root will always be a whole number.

It is easy to find the square root of a perfect square number using a trick. In order to determine the square root without using a long division, we must know the unit digits of squares of the first ten numbers. In the table below, the unit digits are given which are obtained by squaring the numbers from 1 to10.

From the above table, we can figure out that if any perfect square ends with the above digits at the unit place, then its square root will have the same respective number at the unit place. For example, the square root of 81 is 9. It is possible to calculate the square root of a number having 3 digits,4 digits, and 5 digits.

Follow the steps given below to find the square root of the large numbers.

Step 1: Pair the digits starting from right to left.

Step 2: Match the unit digit of the number from the chart and determine the possible values of the square root of the unit digit.

Step 3: Consider the first pair of digits. Let it be “n”.

Step 4: Determine between which two squares this number lies, √a² < n < √b². This concludes that a < n < b. Thus, the tens digit of the desired square root is “a”.

Step 5: As referred to in the chart of squares, there are only two numbers whose squares do not repeat i.e., 5 and 10. Check if the unit digit obtained in step 2 is any of them.

Step 6: Once, it is checked if the obtained number is 5 or 10, then they are written as it is, else we find out the unit digit by using the below steps.

Steps to find units digit if the unit digit obtained in step 2 is apart from 5 or 10 are:

Step 7: Now, multiply a and b.

Step 8: If ab ≤ n, then choose b, else choose a.

Learn about shortcuts to find the square root of a number

Square Root Tricks for 3 Digit Numbers

The square root of a three-digit number is always a two-digit number. Let us learn square root tricks for 3 digit numbers with an example.

Example: Find the square root of 196

Step 1: Split the number into two parts from right to left: 1 96
Step 2: Look at the last digit (6). Perfect squares ending in 6 usually have square roots ending in 4 or 6.
Step 3: Now look at the first part (1). It is the square of 1, so the first digit of the square root will be 1.
Step 4: Choose between 4 and 6. Since 1 is small, we pick the smaller one, which is 4.
Step 5: So, the square root of 196 is 14.

Therefore, √196 = 14.

Learn about how to find square root of a number by division method

Square Root Tricks for 4 Digit Numbers

Let us learn square root tricks for 4 digit numbers with an example.

Example: Find the square root of 2025

Step 1: Split the number into two parts from right to left: 20 25
Step 2: Look at the last two digits (25). Square roots ending in 5 usually end in 5.
Step 3: Now look at the first part (20). The square of 4 is 16 and the square of 5 is 25. Since 20 lies between 16 and 25, the first digit is 4.
Step 4: So, combine the digits: 4 and 5
Step 5: The square root of 2025 is 45

 Therefore, √2025 = 45

Learn about how to find square root of decimal numbers 

Square Root Tricks for 5 Digit Numbers

Let us learn square root tricks for 5 digit numbers with an example.

Example: Find the square root of 10404

Step 1: Pair the digits from right to left: 1 04 04
Step 2: Look at the last two digits (04). Perfect squares ending in 4 may have roots ending in 2 or 8
Step 3: Look at the first part (1). The square of 1 is 1, so the first digit of the square root is 1
Step 4: Choose between 2 and 8. Since 1 is small, choose the smaller one: 2
Step 5: Combine the digits: 1, 0, and 2 → gives 102

 Therefore, √10404 = 102

Learn Square Root of 169 

Square Root Table From 1 to 50

Solved Examples of Square Root Tricks

Example 1: Find the square root of 1521

Solution:

Step 1: Pair the digits from right to left: 15 21

Step 2: The unit digit of 1521 is 1. The square roots of numbers ending in 1 can end in either 1 or 9.

Step 3: Consider the first pair of digits: 15.
15 lies between two perfect squares: 32=9 and 42=16, so the tens digit of the square root is 3.

Step 4: From steps 2 and 3, the possible square roots are 31 or 39.

Step 5: Multiply the tens digit (3) and its next number (4):
3×4=12

Step 6: Since 12 < 15, we choose the greater number from step 4:
Square root of 1521 = 39

Example 2: Find the square root of 24649

Solution:

Step 1: Pair the digits from right to left: 246 49

Step 2: The unit digit is 9. So, the square root could end in 3 or 7.

Step 3: Consider the first group of digits: 246
246 lies between two perfect squares: 152=225 and 162=256 So, the tens digit of the square root is 15

Step 4: From step 2 and 3, the possible square roots are 153 or 157

Step 5: Multiply 15 and 16:
15×16=240

Step 6: Since 240 < 246, we choose the greater number from step 4:
Square root of 24649 = 157

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