Square Root of 3600

The square root of 3600 is 60. The square root of a number with its solution is represented as √3600 = ±60. Consider 60 multiplied by 60 itself or – 60 multiplied by – 60. The product is 3600. Here 3600 is called the perfect square number and ±60 is its square root. ie 60 × 60 or – 60 × – 60 is 3600. 60 will be called the principal square root as it has the positive solution for the given number 3600. Let us find if 60 is the square root for 3600, by using the prime factorisation method, long division method and repeated subtraction method. You can find the ways of Finding Square roots.

Note the Following:

The Square root of 3600 = √3600 where √ = radical, and 3600 is the radicand.

Exponential Form of Square root of 3600 = 3600^1/2

Solution for √3600 = ±60

The Principal Square root = 60

Square root of 3600 is Irrational = False

What is the Square root of 3600?

The square root of 3600 is 60. In other words, the square of 60 is 3600. i.e 60 × 60 is 3600. Also – 60 × – 60 is 3600. 

How to Find the Square root of 3600?

There are three methods to find the Square root of 3600 

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

Square root of 3600 by Prime Factorisation Method

The Square root of 3600 will be obtained only if 3600 is a perfect square number. In this method, let’s divide the number with prime numbers starting with the smallest prime number 2 and increasing the divisors as applicable. The division is continued until the remainder is 1. The prime divisors are grouped into 2 with the same numbers ( as this is a square root) and the groups are multiplied to get the square root.

The given number, 3600 will be expressed as;

3600 = 2 × 2 × 2 × 2 × 3 × 3 × 5 × 5

Grouping into 2 with same divisors: 

Group 1 = 2 × 2, considering only 2

Group 2 = 2 × 2, considering only 2

Group 3 = 3 × 3, considering only 3

Group 4 = 5 × 5, considering only 5

Therefore, the square root of 3600 = 2 × 2 × 3 × 5 = 60.

Square root of 3600 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 3600, grouping it as 36 and 00.

Step 2: Let us find a square number that divides 36

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 

Hence the quotient is the square root of the given number. 

Therefore the Square root of 3600 is 60.

Square root of 3600 by Repeated Subtraction Method.

For finding the square root of 3600 using the repeated subtraction method, 3600 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 3600. Let us find the result in the table below. If the process of repeated subtraction leads to a negative number, then 3600 is not a perfect square number and thus will not have a perfect square root.

For the given number 3600, steps for repeated subtraction are

Since the result of zero is obtained in the 60th Step, the square root of 3600 is 60.

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Solved Examples

1. Which number less than 3600 is a perfect square number?

Solution: 3481 is less than 3600 which is a perfect square number. Its square root is 59.

2. What is the square of 60?

Solution: 60 square is 3600.