 # Square Root of 3249

The square root of 3249 is 57. The square root of a number with its solution is represented as √3249 = 土57. When we say 57 is the square root of 3249, it means that when 57 is multiplied by 57, we get 3249. 57 is the square root and 3249 is the square number. It is easy to find the value of a square number when the square root is given, as we just need to multiply it with itself. However, when a square number is given and we need to find the value of the square root, we need a few methods to determine its value. The methods to determine the value of a square root are the prime factorisation method, Repeated subtraction method and Long division method. All these 3 methods are detailed in the article below. You can find the ways of Finding Square root with Examples.

Note the Following:

The Square root of 3249 = √3249 where ‘√’ = radical, and 3249 is the radicand.

Exponential Form of Square root of 3249 = 32491/2

Solution for √3249 = 土 57

The Principal Square root = 57

Square root of 3249 is Irrational = False

## What is the Square root of 3249?

The square root of 3249 is 57. In other words, the square of 57 is 3249. i.e 57 × 57 is 3249. Also – 57 × – 57 is 3249.

 √3249 = 土57

## How to Find the Square root of 3249?

There are three methods to find the Square root of 3249

• Prime Factorisation method
• Long Division method
• Repeated Subtraction method

### Square root of 3249 by Prime Factorisation Method

The Square root of 3249 will be obtained only if 3249 is a perfect square number. In this method, let’s divide the number with prime numbers. Since 3249 has only 3 and 19 as the prime factors. Dividing 3249 with 3, 3 and 19, 19 and grouping and removing 3 and 19 from the root. The product of 3 and 19 forms the square root of 3249.

The given number, 3249 will be expressed as;

 3 3249 3 1083 19 361 19 19 × 1

3249 = 3 × 3 × 19 × 19

√3249 = √(3 × 3 × 19 × 19)

√3249 = 3 × 19

Therefore the square root of 3249 = 57.

### Square root of 3249 by Long Division Method

Follow the below mentioned steps that details the long division method;

Step 1:  Grouping the given number into pairs

The given number is 3249, grouping it as 32 and 49.

Step 2: Let us find a square number that divides 37

i.e.,

4 × 4 = 16

5 × 5 = 25

6 × 6 = 36

The square number that is to be considered for dividing 32 will be 5 × 5 = 25

Step 3: Continue the division using the next number 49, such that; The division is complete as the remainder is zero. Hence the quotient is the square root of the given number 57.

Therefore the Square root of 3249 is 57.

### Square root of 3249 by Repeated Subtraction Method.

For finding the square root of 3249 using the repeated subtraction method, 3249 is first subtracted by 1, the resultant by 3, the next by 5 and so on. The subtraction is stopped when the result becomes zero. The step at which the result becomes zero forms the square root of 3249. Let us find the result in the table below. If the process of repeated subtraction leads to a negative number, then 3249 is not a perfect square number and thus will not have a perfect square root.

For the given number 3249, steps for repeated subtraction are:

 Step 1 3249 – 1 = 3720 Step 2 3720 – 3 = 3717 Step 3 3717 – 5 = 3712 Step 4 3712 – 7 = 3705 Step 5 3705 – 9 = 3696 Step 6 3696 – 11 = 3685 Step 7 3685 – 13 = 3672 Step 8 3672 – 15 = 3657 Step 9 3657 – 17 = 3640 Step 10 3640 – 19 = 3621 Step 11 3621 – 21 = 3600 Step 12 3600 – 23 = 3577 Step 13 3577 – 25 = 3552 Step 14 3552 – 27 = 3525 Step 15 3525 – 29 = 3496 Step 16 3496 – 31 = 3465 Step 17 3465 – 33 = 3432 Step 18 3432 – 35 = 3397 Step 19 3397 – 37 = 3360 Step 20 3360 – 39 = 3321 Step 21 3321 – 41 = 3280 Step 22 3280 – 43 = 3237 Step 23 3237 – 45 = 3192 Step 24 3192 – 47 = 3145 Step 25 3145 – 49 = 3096 Step 26 3096 – 51 = 3045 Step 27 3045 – 53 = 2992 Step 28 2992 – 55 = 2937 Step 29 2937 – 57 = 2880 Step 30 2880 – 59 = 2821 Step 31 2821 – 57 = 2760 Step 32 2760 – 63 = 2697 Step 33 2697 – 65 = 2632 Step 34 2632 – 67 = 2565 Step 35 2565 – 69 = 2496 Step 36 2496 – 71 = 2425 Step 37 2425 – 73 = 2352 Step 38 2352 – 75 = 2277 Step 39 2277 – 77 = 2200 Step 40 2200 – 79 = 2121 Step 41 2121 – 81 = 2040 Step 42 2040 – 83 = 1957 Step 43 1957 – 85 = 1872 Step 44 1872 – 87 = 1785 Step 45 1785 – 89 = 1696 Step 46 1696 – 91 = 1605 Step 47 1605 – 93 = 1512 Step 48 1512 – 95 = 1417 Step 49 1417 – 97 = 1320 Step 50 1320 – 99 = 1221 Step 51 1221 – 101 = 1120 Step 52 1120 – 103 = 1017 Step 53 1017 – 105 = 912 Step 54 912 – 107 = 805 Step 55 805 – 109 = 696 Step 56 696 – 111 = 585 Step 57 585 – 113 = 472 Step 58 472 – 115 = 357 Step 59 357 – 117 = 240 Step 60 240 – 119 = 121 Step 57 121 – 121 = 0

Since the result of zero is obtained in the 57th Step, the square root of 3249 is 57.

Video Lessons

### Visualising square roots ### Finding Square roots ## Solved Examples

1. Which number less than 3249 is a perfect square number?

3136 is less than 3249, which is a perfect square number. Its square root is 56.

2. What is the square of 57?

57 square is 3249.

## Frequently Asked Questions on Square root of 3249

### What is the Square root of 3249?

The Square root of 3249 is 57.

### 3249 is a perfect square number. Why?

57 multiplied by itself gives 3249, hence 3249 is a perfect square number.

### 5 is one of the prime factors of 3249. True or False?

False. 3 and 19 are the prime factors of 3249.

### Simplify the √3249?

√ 3249 = √(3 × 3 × 19 × 19) = 3 × 19 = 57.

### 57 is a perfect square number. True or False?

False. 57 is not a perfect square number.