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Square root tricks are those tricks that are helpful in solving square root related questions. Knowing square root tricks to find the square root 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 the class 8 syllabus.

## Definition of Square Root

The square root of a number is the number that on squaring results the given number. It is represented using this symbol "√". The square root of a number can be a rational number or an irrational number. If the square root of a number is a whole number, then it is a perfect square. In order to calculate the square root of a number easily, square root tricks are used. Let's find out more about it.

## Tricks to Calculate Square Root

We can estimate 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.

It is possible to calculate the square root of a number having 4 digits as well as 5 digits. Let us learn to calculate the square root of numbers using the trick.

### Square Root Trick for 4 Digit Numbers

The steps to estimate the square root of a 4 digit number are:

• Step 1: Pair the digits starting from right to left.
• Step 2: Match the unit digit of number from the chart and determine the possible values of the square root of the unit digit.
• Step 3: Let us 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 anyone 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.

Example: Find the square root of 1521.
Solution: The steps to determine the square root of 1521 are:

• The digits of 1521 are paired as 15 21.
• The unit digit of 1521 is 1. Hence, the possible unit digits, as per the chart, after taking the square root could be 1 and 9.
• Let us consider the pair of digits 15.
• The number 15 lies between two perfect squares 9 and 16 that is, 9 < 15 < 16 which can be written as 32 < 15 < 42. Hence, the tens digit of the square root of 1521 is 3 since 3 < 4.
• As the number obtained in step 2 is, 1 and 9.  The numbers can be 31 or 39.
• The product of the possible tens digits gives the value 12 (as here a = 3 and b = 4).
• As 12 < 15, the square root of 1521 will be the greater of 31 and 39 which is 39.

### Square Root Trick for 5 Digit Numbers

The steps to estimate the square root of a 5 digit number are:

• Step 1: First pair the digits starting from right to left.
• Step 2: Match the unit digit of number from the chart and determine the possible values of the square root of the unit digit.
• Step 3: Let us consider the group of the first three 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 anyone among 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 steps below.

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.

Example: Find the square root of 10816.
Solution: The steps to determine the square root of 10816 are:

• The digits of 10816 are paired as 108 16.
• The unit digit of 10816 is 6. Hence, the possible unit digits after taking square root could be 4 and 6.
• When we consider the first three digits of 10816, that are 108.
• The number 108 lies between two perfect squares 100 and 121 that is, 100 < 108 < 121 which can be written as 102 < 108 < 112. Hence, the tens digit of the square root of 10816 is 10 as 10 < 11.
• As the number obtained in step 2 is, 4 and 6.  The numbers can be 104 or 106.
• 108 lies between 102 and 112. Their product gives the value 110.
• As the 110 > 108, the square root of 10816 will be the lesser of 104 and 106 which is 104. 