How to find the Square Root of a number

 One such trick that will help you solve many numerical problems is finding the square root. As in competitive examinations often calculation based questions are asked. Here in this article, you will know how to find the square root of a number.

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.

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Tricks to Find Square Root

The tricks to find the square root of perfect squares is very easy to remember. We need to keep in mind the unit place digit of squares of numbers from 1 to 10. So, we find out the unit digit....

The unit digit of square number of 1 is 1.

The unit digit of square number of 2 is 4.

The unit digit of square number of 3 is 9.

The unit digit of square number of 4 is 6.

The unit digit of square number of 5 is 5.

The unit digit of square number of 6 is 6.

The unit digit of square number of 7 is 9.

The unit digit of square number of 8 is 4.

The unit digit of square number of 9 is 1.

The unit digit of square number of 10 is 0.

Hence, from the above we can figure out 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 49 is 7.

Square root Tricks for 3-digit Numbers

The square root of a three-digit number is always a two-digit number. Let us learn to find the square root with an example.

Example:-

Square root of 196: 

Pair the digits from the right-hand side: 1 and 96.

The unit place of 196 is 6. So, either the square root will have 4 or 6 at the unit place

Now, considering the first digit, 1, it is the square of 1. Thus, the first digit of the square root of 196 is 1.

Since 1 is the smallest number of the square. Hence, the square root of 196 will take a smaller number between 4 and 6. Thus, it will be 4.

Hence, the required square root is 14.

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Square root Tricks for 4-digit Numbers

      If the number is 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 3589.

Step 1: The unit digit in this number is 9, which can be a unit digit of its square root number such as 3 or 7.

Step 2: Now let us consider the first two digits that is 35 which comes between the squares of 5 and 6 because 25 < 35< 36.

Step 3: We can assume that the ten’s digit of the square root of 3589 is the lowest among the two numbers 5 and 6 is 5, and we need to find the unit digit of the square root of the number 3589.

Step 4: Now, we need to find between 53 or 57 which is the square root of 3589.

Step 5: Since the ten’s digit is 5 and the next number is 6, we need to multiply both the numbers like 5 x 6 = 30 and since 30 is less than 35.

Step 6: Square root of 3589 will be the bigger number between 53 and 57 i.e. 57.

Therefore, \(\sqrt{3589}\) = 57.

Example 2:

 Let us 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.

Now let’s consider the first two digits that is 70 which comes between the squares of 8 and 9 because of 64< 70 <81

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, \(\sqrt{7056} = 84\).

Square Root of 5-Digit Numbers

To find the square root of a 5-digit number, follow the below steps with the help of an example.

Example: Find the square root of 40401.

Step 1: Pair the digits from right to left, 404 and 01.

Step 2: Check the unit digit of the number and compare it with the above table. Here, the unit digit is 1, thus possible unit digits for the square root of 40401 is 1 and 9. But the square root of 1 is 1, thus unit digit will have 1.

Step 3: Now, the first three digits are 404. It will lie between 400 < 404 < 441. Hence, the square root of first three digit will be near to 20.

Step 4: Hence, the required square root is 201

Note:- similar way we can find out the square root of 6 digit number and so on.

Example:- 

1. Find the square root of 6241 using the square root tricks.

2. Find the square root of 735305 using the square root tricks.