Square Root Tricks

The square root is a complex operation. Hence, it can be a time-consuming operation to obtain the square roots of a number. There are small tricks that can be used to determine the square root of a number faster. Stay tuned to learn such tricks and see the speed of your calculation increase!!!

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. 

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. 

Topics Related to Square Root Tricks

• Perfect Squares
• Square Root of 10 
• Square Root of 19
• Square Root Worksheets
• Squares and Square Roots Worksheets
• Perfect Squares Worksheets

What is Square Root in Math?

The square root is an arithmetic operation represented by a symbol √ and its value is the number that on squaring gets results from the given number. For example, square root of 4 is 2 as √4 = √(2²) = 2.

What is the Trick to Find Square Root?

The square root of a number can be found by using the below steps:

• 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: Now, we consider the first set of digits of the number.
• Step 4: It is determined that between squares of which two numbers the first set digits of number lies. The number whose square results in a number lower than the given number is chosen as the tens digit of the square root of a given number.
• 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 below steps.

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

• Step 7: The numbers between which the first set of digits lie are multiplied.
• Step 8: If the number obtained is less than the given number the greater of the two numbers is chosen while if the number obtained is more than the given number the lesser of two numbers is chosen.

How Do You Find the Square Root of a 3 Digit Number Using Square Root Tricks?

The square root of a 3 digit number is always a 2 digit number. Hence in order to understand using square root tricks for a 3 digit number, let us consider taking the square root of 324.

• The digits of 324 are paired as 3 24.
• The unit digit of 324 is 4. Hence, the possible unit digits after taking square root could be 2 and 8.
• When we consider the first digit of 324, that is 3.
• The number 3 lies between 1 and 2 that is, 1 < 3 < 4 which can be written as 1² < 3 < 2². Hence, the tens digit of the square root of 324 is 1.
• As the number obtained in step 2 is, 2 and 8.  The numbers can be 12 or 18.
• In order to determine the square root of 324, we multiply the tens and one's digits in both cases. 
• 3 lies between 1² and 2². Their product gives the value 2.
• As the 2 < 3, the square root of 324 will be the greater of 12 and 18 which is 18. 

Thus, the square root of 324 is 18.

What is the Easiest Way to Find the Square Root of a 4 Digit Number?

The Easiest Way to Find the Square Root of a 4 Digit Number is by using square root tricks.

• Step 1: First we pair the digits starting from right to left.
• Step 2:Now, the unit digit of the number is matched with the chart and the possible values of the square root of the unit digit are determined. 
• Step 3: We consider the first two digits of the number.
• Step 4: It is determined that the first two digits of a number lie between squares of which two numbers. The number whose square results in a number lower than the given number is chosen as the tens digit of the square root of a given number.
• Step 5: There are only two numbers whose squares do not repeat i.e, 5 and 10 in the chart of squares. 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: The numbers between which the first two digits lie are multiplied.
• Step 8: If the number obtained is less than the given number the greater of the two numbers is chosen while if the number obtained is more than the given number the lesser of two numbers is chosen.

Is the Square root of 169 a Whole Number?

Yes, the square root of 169 is a whole number as √169 = 13.