Competitive exams have at least one question where you have to find the square root of a number in seconds. With the help of this **shortcut method, **you can **find square root of a number** within seconds. This method is applicable only for perfect squares. The Square root questions asked in competitive exams/bank exams & entrance exams are usually perfect squares. Refer How to check if a number is a perfect square? to find out if a given number is a perfect square.

**How to Find Square Root Easily Using Shortcut**

Below are the steps to find square root of a number easily in seconds.

**Step 1:** First, group the number in pairs of 2 starting from the right.

**Step 2:** To get the ten’s place digit, Find the nearest square (equivalent or greater than or less than) to the first grouped pair from the left and put the square root of the square.

**Step 3: **To get the unit’s place digit of the square root value.

Remember the following

If the number ends in | Unit’s place digit of the square root |

1 | 1 or 9(10-1) |

4 | 2 or 8(10-2) |

9 | 3 or 7(10-3) |

6 | 4or 6(10-4) |

5 | 5 |

0 | 0 |

Let’s see the logic used in this method of How to find square root using short cut for a better understanding

We know,

1^{2}=1

2^{2}=4

3^{2}=9

4^{2}=16

5^{2}=25

6^{2}=36

7^{2}=49

8^{2}=64

9^{2}=81

10^{2}=100

Now, observe the unit’s place digit of all the squares. Do you find anything common?

We notice that,

Unit’s place digit of both 1^{2}and 9^{2 }is 1.

Unit’s place digit of both 2^{2} and 8^{2} is 4.

And Unit’s place digit of both 3^{2} and 7^{2} is 9

Unit’s place digit of both 4^{2} and 6^{2} is 6.

**Step 4:** Multiply the ten’s place digit (found in step 1) with its consecutive number and compare the result obtained with the first pair of the original number from the left.

**Remembe**r,

**If the first pair of the original number > Result obtained on multiplication then select the greater number out of the two numbers as the unit’s place digit of the square root.
If the first pair of the original number < the result obtained on multiplication, then select the lesser number out of the two numbers as the unit’s place digit of the square root.
Let us consider an example to get a better understanding of this method on how to find square root of any number quickly.**

**How to find square root of a 3 Digit Number**

**Example 1: √784=?**

**Step 1:** We start by grouping the numbers in pairs of two from the right as follows

**7 84**

**Step 2:** To get the ten’s place digit,

The nearest square to the first group (7) is 4 and √4=2 Therefore, ten’s place digit=2.

**Step 3:** To get the unit’s place digit,

We notice that the number ends with 4, So the unit’s place digit of the square root should be either 2 or 8(Refer to the table).

**Step 4:** Multiplying the ten’s place digit of the square root that we arrived at in step 1(2) and its consecutive number(3) we get 2 x 3=6

ten’s place digit of original number > Multiplication result

7>6

So we need to select the greater number (8) as the unit’s place digit of the square root.

Unit’s place digit =8

**Ans:√784=28**

**How to find square root of any 4 digit number**

**Example 2: √3721?**

**Step 1:** We start by grouping the numbers in pairs of two from the right as follows

**37 21**

**Step 2:** To get the ten’s place digit,

We find that the nearest square to the first group (37) is 36 and √36=6 Therefore, ten’s place digit=6.

**Step 3:** To get the unit’s place digit,

We notice that the number ends with 1, So the unit’s place digit of the square root should be either 1 or 9(Refer to the table).

**Step 4: **Multiplying the ten’s place digit of the square root that we arrived at in step 1(6) and its consecutive number(7) we get,

**6 x 7=42**

ten’s place digit of an original number<Multiplication result

37 < 42

So we need to select the lesser number (1) as the unit’s place digit of the square root.

Unit’s place digit =1

**Ans:√3721=61**

**How to find Square Root Easily using shortcut Method**

**Example 3: √6889?**

**Step 1:** We start by grouping the numbers in pairs of two from the right as follows

**68 89**

**Step 2: **To get the ten’s place digit,

The nearest square to the first group (68)is 64 and√64=8. Therefore ten’s place digit=8

**Step 4:** Multiplying the ten’s place digit of the square root that we arrived at in step 1(8) and its consecutive number(9) we get,

8 x 9 =72

ten’s place digit of an original number<Multiplication result

68 < 72

So we need to select the lesser number (3) as the unit’s place digit of the square root.

Unit’s place digit =3

**Ans:√6889=83**

**How to Find square root of 5 digit number**

**Example 4: √64516**

**Step 1:** We start by grouping the numbers in pairs of two from the right as follows

**645 16**

**Step 2:** To get the ten’s place digit,

We find that the nearest square to the first group (645)is 625 and√625=25

Therefore ten’s place digit=25

**Step 3:** To get the unit’s place digit,

We notice that the number ends with 6, So the unit’s place digit of the square root should be either 4 or 6(Refer to the table).

**Step 4:** Multiplying the ten’s place digit of the square root that we arrived at in step 1(25)and its consecutive number(26)

we get, 25 x 26=650

ten’s place digit of an original number<Multiplication result

645< 650

So we need to select the lesser number (4) as the unit’s place digit of the square root.

Unit’s place digit =4

**Ans:√64516=254**

**How to find square root of any 6 digit number**

**Example 5: √126736**

**Step 1:** We start by grouping the numbers in pairs of two from the right as follows. For a 6 digit number, this is how it should be paired.

**1267 36**

**Step 2: **To get the ten’s place digit,

We find that the nearest square to the first group (1267)is 1225 and√1225=35

Therefore ten’s place digit=35

**Step 3:** To get the unit’s place digit,

We notice that the number ends with 6, So the unit’s place digit of the square root should be either 4 or 6(Refer to the table).

**Step 4:** Multiplying the ten’s place digit of the square root that we arrived at in step 1(35)and its consecutive number(36)we get,

35 x 36=1260

ten’s place digit of original number>Multiplication result

1267>1260

So we need to select the greater number (6) as the unit’s place digit of the square root.

Unit’s place digit =6

**Ans:√126736=356**

**Example 6: √207025**

**Step 1:** We start by grouping the numbers in pairs of two from the right as follows. For a 6 digit number, this is how it should be paired.

**2070 25**

**Step 2:** To get the tenth place digit,

The nearest square to the first group (2070) is 2025 and√2025=45.

Therefore ten’s place digit=45

**Step 3:** To get the unit’s place digit,

We notice that the number ends with 5, So the unit’s place digit of the square root should be 5(Refer to the table).

Skip all the other steps that are to be used in how to find square root for a number ending in 5

Unit’s place digit =5

**Ans:√207025=455**

**Square root 1 to 25/** **Square Root 1 to 30**

Number | Square Root of Given Number |

1 | 1 |

2 | 1.41 |

3 | 1.73 |

4 | 2 |

5 | 2.23 |

6 | 2.44 |

7 | 2.64 |

8 | 2.82 |

9 | 3 |

10 | 3.16 |

11 | 3.31 |

12 | 3.46 |

13 | 3.6 |

14 | 3.74 |

15 | 3.87 |

16 | 4 |

17 | 4.12 |

18 | 4.24 |

19 | 4.35 |

20 | 4.47 |

21 | 4.58 |

22 | 4.69 |

23 | 4.79 |

24 | 4.89 |

25 | 5 |

26 | 5.09 |

27 | 5.20 |

28 | 5.29 |

29 | 5.39 |

30 | 5.48 |

You may also refer to the square root table 1 to 50.

**How to Find Square root using Square Root Formula**

** n√z = z**^{ 1/n}

^{ 1/n}

So here, if we substitute number 2 for n. Then it would be the square root of z.

To Generalise, the above formula can be used to find the nth root of any given number z.

**How to Find Square root of a Decimal Number?**

You may use the same shortcut “How to find square root on whole numbers” to find square root of a decimal number.

Below are the steps:

**Step 1:** First, group the number in pairs of 2 starting from the right.

**Step 2:** To get the ten’s place digit, Find the nearest square (equivalent or greater than or less than) to the first grouped pair from the left and put the square root of the square.

**Step 3: **To get the unit’s place digit of the square root value.

**Step 4:** Place the decimal point after the ten’s place digit.

We shall apply the same shortcut to the previous examples with a decimal point added to understand how it works

**Example 1: √7.84=**?

**Step 1:** We start by grouping the numbers in pairs of two from the right as follows

**7 84**

**Step 2:** To get the ten’s place digit,

The nearest square to the first group (7) is 4 and √4=2 Therefore, ten’s place digit=2.

**Step 3:** To get the unit’s place digit,

We notice that the number ends with 4, So the unit’s place digit of the square root should be either 2 or 8(Refer to the table).

**Step 4:** Multiplying the ten’s place digit of the square root that we arrived at in step 1(2) and its consecutive number(3) we get 2 x 3=6

ten’s place digit of original number > Multiplication result

7>6

So we need to select the greater number (8) as the unit’s place digit of the square root.

Unit’s place digit =8

Step 5: Now, place the decimal point after the ten’s place digit (2)

**Ans:√7.84=2.8**

**Example 2: √37.21?**

**Step 1: **Grouping in pairs

**37 21**

**Step 2:** Find the ten’s place digit which is 6.

**Step 3:** Find the unit’s place digit which is 1.

**Step 4:** Now, place the decimal point next to the ten’s place digit to arrive at your answer.

**Ans:√37.21=6.1**

**Faqs**

### (1) Can I use the shortcut method to find square root of a decimal number?

Yes, you can use the same shortcut method to find square root of a decimal number. The only condition is you must ensure that the decimal point is placed exactly at the place where the number is grouped. If the decimal point is placed differently, then you cannot apply the shortcut method.

### (2) If the decimal point is placed differently then how to find square root of the decimal number?

You may use the long division method to find the square root.

### (3) Can I use the shortcut method to find square root of perfect and non-perfect squares?

You will get accurate results if you apply “how to find square root of a number” on perfect squares only. You may need to use the long division method to find square root of non-perfect squares to get accurate results.

### (4) What is the easiest way to find square root of a number?

Using the above shortcut method to find square root of a number is the easiest.

### (5) What is the square root of 3?

Square root of 3 is 1.73.

### (6)What is the value of root 2?

Root 2 is an irrational number as it cannot be expressed as a fraction. Therefore, usually, the value of root 2 is assumed to be 1.414 in mathematical calculations.

### (7)What is the square root of 8?

8 is a non-perfect square. So, as per the table, the Square root 8 value is 2.82.

### (8)What is the square root of 6?

6 is a non-perfect square. So, as per the table, the value of root 6 is 2.44.

### (9)What is root 10 value?

10 is a non-perfect square. So, as per the table, the Square root of 10 is 3.16.

### (10)What is the square root of 25?

The number 25 is a perfect square. So, using the “how to find square root shortcut” the square root of 25 is 5.

### (11)What is the square root of 20?

20 is a non-perfect square. So, as per the table, the Square root of 20 is 4.47.

### (12)What is the square root of 100?

The number 100 is a perfect square. So, using the “how to find square root shortcut” the square root of 100 is 10.

### (13)What is 30 square root?

30 is a non-perfect square. So, as per the table, the Square root of 30 is 5.48.

### (14)Whats the square root of 9?

The number 9 is a perfect square. So, using the “how to find square root shortcut” the square root of 9 is 3.

### (15)What is root 1 value?

As 1 is a real number, we can assume the square root of 1 as 1 itself.

### (16)How to find root value?

You may use the “how to find square root shortcut” on perfect squares to find the root value. And you may use the long division method to find the root value on non-perfect squares.

### (17)What is square root of 2025?

The number 2025 is a perfect square. So, using the “how to find square root shortcut” the square root of 2025 is 45.

### (18)How to find square root without calculator?

You may use either the shortcut method “how to find shortcut of a number easily” or the long division method to find the square root of a number without using a calculator.

### (19)What is the square root of 45?

45 is a non-perfect square. So, as per the table, the Square root of 45 is 6.71.

In a nutshell, you can use how to find square root shortcut on the whole number and a decimal number. With these simple tricks and tips, you are sure to rock your exams.