Square Root of 3721

The square root of 3721 is 61. The square root of a number with its solution is represented as √3721 = ±61. When a number is multiplied by itself, the product is termed as the square number. To determine the square root of 3721, we need to identify the number x, such that x × x = 3721. Note that the value of x can be either positive or negative as it is being multiplied by itself. The product, however, will be positive only. The methods to determine the value of x are the prime factorization method, Repeated subtraction method and Long division method. All these 3 methods are detailed in the article below. You can find ways of Finding Square roots.

Note the Following:

The Square root of 3721 = √3721 where ‘√’ = radical, and 3721 is the radicand.

Exponential Form of Square root of 3721 = 3721^1/2

Solution for √3721 = ±61

The Principal Square root = 61

Square root of 3721 is Irrational = False

What is the Square root of 3721?

The square root of 3721 is 61. In other words, the square of 61 is 3721. i.e., 61 × 61 is 3721. Also, – 61 × – 61 is 3721. 

How to Find the Square root of 3721?

There are three methods to find the Square root of 3721 

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

Square root of 3721 by Prime Factorisation Method

The Square root of 3721 will be obtained only if 3721 is a perfect square number. In this method, let’s divide the number with prime numbers. Since 3721 has only 1, 61 and 3721 as the prime factors. Dividing 3721 with 61, and grouping 61 and removing 61 from the root forms the square root of 3721.

The given number, 3721 will be expressed as;

3721 = 61 × 61

√3721 = √(61 × 61)

√3721 = 61

Therefore the square root of 3721 = 61.

Square root of 3721 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 3721, grouping it as 37 and 21.

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 36 will be 6 × 6 = 36

Step 3: Continue the division using the next number 21

The division is complete as the remainder is zero. Hence the quotient is the square root of the given number which is 61. 

Therefore the Square root of 3721 is 61.

Square root of 3721 by Repeated Subtraction Method.

For finding the square root of 3721 using the repeated subtraction method, 3721 is first subtracted by 1, the resultant by 3, the next resultant by 5 and so on. The subtraction is stopped when the resultant becomes zero. The step at which the result becomes zero, forms the square root of 3721. Let us find the result in the table below. If the process of repeated subtraction leads to a negative number, then 3721 is not a perfect square number and thus will not have a perfect square root.

For the given number 3721, steps for repeated subtraction are

Since the result of zero is obtained in the 61th Step, the square root of 3721 is 61.

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Solved Examples

1. Which number less than 3721 is a perfect square number?

3600 is less than 3721 which is a perfect square number. Its square root is 60.

2. What is the square of 61?

61 square is 3721.