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 = 3249^1/2

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. 

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;

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:

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

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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.