Square Root of 2704

The square root of 2704 is 52. The square root of a number with its solution is represented as √2704 = 土52. Consider 52 multiplied by 52 itself or – 52 multiplied by – 52. The product is 2704. Here 2704 is called the perfect square number and 土52 is its square root. ie 52 × 52 or – 52 × – 52 is 2704. 52 will be called the principal square root as it has the positive solution for the given number 2704. Let us find if 52 is the square root for 2704 by using the prime factorisation method, long division method and repeated subtraction method. You can find ways of Finding Square roots.

Note the Following:

The Square root of 2704 = √2704 where ‘√’ = radical, and 2704 is the radicand.

Exponential Form of Square root of 2704 = 2704^1/2 

Solution for √2704 = 土52

The Principal Square root = 52

Square root of 2704 is Irrational = False

What is the Square root of 2704?

The square root of 2704 is 52. In other words, the square of 52 is 2704. i.e., 52 × 52 is 2704. Also – 52 × – 52 is 2704. 

How to Find the Square root of 2704?

There are three methods to find the Square root of 2704 

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

Square root of 2704 by Prime Factorisation Method

The Square root of 2704 will be obtained only if 2704 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 as applicable. The division is continued till the remainder is 1. The prime divisors are grouped into 2 with the same numbers (as this is square root) and the groups are multiplied to get the square root.

The given number, 2704 will be expressed as;

2704 = 2 × 2 × 2 × 2 × 13 × 13

Grouping into 2 with same divisors: 

Group 1 = 2 × 2, considering only 2

Group 2 = 2 × 2, considering only 2

Group 3 = 13 × 13, considering only 13

Therefore, the square root of 2704 = 2 × 2 × 13 = 52.

Square root of 2704 by Long Division Method

Follow the below-mentioned steps that detail the long division method;

Step 1:  Grouping the given number into pairs

The given number is 2704, grouping it as 27 and 04.

Step 2: Consider the first number, which is 27.

Let us find a square number that divides 27

i.e., 

1 × 1 = 1 

2 × 2 = 4

3 × 3 = 9

4 × 4 = 16

5 × 5 = 25 

6 × 6 = 36 

The square number that is to be considered for dividing 27 will be 5 × 5 = 25

Step 3: Dividing 27 by 5

 Step 4: Continue the division using the next number 04

 The first number to be used as the next divisor is 5 + 5 = 10 (Divisor of first division + quotient of first division) 

Now considering a two digit number starting with 10 to divide 204 will be:

101 × 1 = 101

102 × 2 = 204

Continue the division as: 

Further division is not possible as the remainder is zero. Hence the quotient is the square root of the given number. 

Therefore the Square root of 2704 is 52.

Square root of 2704 by Repeated Subtraction Method.

For finding the square root of 2704 using repeated subtraction method, 2704 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 2704. Let us find the result in the table below. 

For the given number 2704, steps for repeated subtraction are:

Since the result of zero is obtained in the 52th Step, the square root of 2704 is 52.

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Solved Examples

1. What is the square root of 4?

2 is the square root of 4.

2. What is the square root of 27?

The square root of 27 is 5.196.