# Square Root Tricks

**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.

## 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, 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.

## 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. Find the unit digits we get after squaring the numbers from 1 to 10 in the below table.

Number |
Unit digit of Number^{2} |

1 | 1 |

2 | 4 |

3 | 9 |

4 | 6 |

5 | 5 |

6 | 6 |

7 | 9 |

8 | 4 |

9 | 1 |

10 | 0 |

Hence, from the above table 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 81 is 9.

## Square root Tricks of 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.

**Square root of 144: **

- Pair the digits from the right-hand side:
**1 44** - The unit place of 144 is 4. So, either the square root will have 2 or 8 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 144 is 1.
- Since 1 is the smallest of the square. Hence, the square root of 144 will take a smaller number between 2 and 8. Thus, it will be 2.
- Hence, the required square root is 12.

**Try More:**

- Square root of 169 = 13
- Square root of 225 = 15
- Square root of 324 = 18

## Square Root Tricks of 4-Digit Numbers

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 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 such as 3 or 7. Because 3^{2}is 9 and 7^{2}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 6^{2}< 44< 7^{2}**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 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 because 4
^{2}is 16 and 6^{2}is 36 - Now let’s consider the first two digits that is 70 which comes between the squares of 8 and 9 because of 8
^{2}< 70 <9^{2} - 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

## 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 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 20^{2}and 21^{2}. Thus, 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

## Square Root Table 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 |

## Related Articles

- Square Root
- Square Root Questions
- Square Root of 289
- Square Root of 576
- Squares and Square Roots
- Square Root Formula
- Square Root Table
- Square Root Long Division Method
- Square Root Prime Factorization

## Solved Examples

**Q.1: What is the square root of 25?**

Solution: The square root of 25 is 5.

25 = 5 x 5 = 5^{2}

Taking the root we get;

√5^{2} = 5

**Q.2: What is square root of 625?**

Solution: The square root of 625 is 25.

625 = 5 x 5 x 5 x 5 = 25 x 25 = 25^{2}

Taking the root we have;

√625 = √25^{2} = 25