 # 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 = 36001/2

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.

 √3600 = ±60

## 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;

 2 3600 2 1800 2 900 2 450 3 225 3 75 5 25 5 5 × 1

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

 Step 1 3600 – 1 = 3599 Step 2 3599 – 3 = 3596 Step 3 3596 – 5 = 3591 Step 4 3591 – 7 = 3584 Step 5 3584 – 9 = 3575 Step 6 3575 – 11 = 3564 Step 7 3564 – 13 = 3551 Step 8 3551 – 15 = 3536 Step 9 3536 – 17 = 3519 Step 10 3519 – 19 = 3500 Step 11 3500 – 21 = 3479 Step 12 3479 – 23 = 3456 Step 13 3456 – 25 = 3431 Step 14 3431 – 27 = 3404 Step 15 3404 – 29 = 3375 Step 16 3375 – 31 = 3344 Step 17 3344 – 33 = 3311 Step 18 3311 – 35 = 3276 Step 19 3276 – 37 = 3239 Step 20 3239 – 39 = 3200 Step 21 3200 – 41 = 3159 Step 22 3159 – 43 = 3116 Step 23 3116 – 45 = 3071 Step 24 3071 – 47 = 3024 Step 25 3024 – 49 = 2975 Step 26 2975 – 51 = 2924 Step 27 2924 – 53 = 2871 Step 28 2871 – 55 = 2816 Step 29 2816 – 57 = 2759 Step 30 2759 – 59 = 2700 Step 31 2700 – 61 = 2639 Step 32 2639 – 63 = 2576 Step 33 2576 – 65 = 2511 Step 34 2511 – 67 = 2444 Step 35 2444 – 69 = 2375 Step 36 2375 – 71 = 2304 Step 37 2304 – 73 = 2231 Step 38 2231 – 75 = 2156 Step 39 2156 – 77 = 2079 Step 40 2079 – 79 = 2000 Step 41 2000 – 81 = 1919 Step 42 1919 – 83 = 1836 Step 43 1836 – 85 = 1751 Step 44 1751 – 87 = 1664 Step 45 1664 – 89 = 1575 Step 46 1575 – 91 = 1484 Step 47 1484 – 93 = 1391 Step 48 1391 – 95 = 1296 Step 49 1296 – 97 = 1199 Step 50 1199 – 99 = 1100 Step 51 1100 – 101 = 999 Step 52 999 – 103 = 896 Step 53 896 – 105 = 791 Step 54 791 – 107 = 684 Step 55 684 – 109 = 575 Step 56 575 – 111 = 464 Step 57 464 – 113 = 351 Step 58 351 – 115 = 236 Step 59 236 – 117 = 119 Step 60 119 – 119 = 0

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

## Video Lessons

### Visualising square roots ### Finding Square roots ## 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.

## Frequently Asked Questions on Square root of 3600

### What is the Square root of 3600?

The Square root of 3600 is 60.

### 3600 is a perfect square number. Why?

60 multiplied by itself gives 3600, hence 3600 is a perfect square number.

### 5 is one of the prime factors of 3600. True or False?

True. 5 is also a prime factor of 3600.

### What is 60 square?

60 square is 3600.

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

False. 60 is not a perfect square number.