Square Root of 53
Square root of 53 is a number which, when multiplied by itself, results in the number 53. 53 is an odd number and a prime number. Prime numbers have been described as the building blocks of mathematics. Let us determine the square root of 53 in this article. We will learn how to calculate the square root of 53, find out whether square root of 53 a rational or irrational, and look at a few problems to help us understand this topic.
 Square Root of 53: √53 = 7.280
 Square of 53: 53^{²} = 2809
1.  What Is the Square Root of 53? 
2.  Is Square Root of 53 Rational or Irrational? 
3.  How to Find the Square Root of 53? 
4.  Challenging Questions 
5.  FAQs on Square Root of 53 
What Is the Square Root of 53?
The square root of a number n is written as √n. This number when squared or multiplied by itself results in the original number n. The square root of 39 can be written as:
 Radical form: √53
 Decimal form: 7.280
 Exponent form: (53)^{1/2}
Is Square Root of 53 Rational or Irrational?
 53 is a number that is not a perfect square, meaning it does not have a natural number as its square root.
 Square root of 53 is simlipfied in decimal form as √53 = 7.280.
 Square root of 53 cannot be expressed as a fraction in the form p/q which tells us that the square root of 53 is an irrational number.
How to Find the Square Root of 53?
There are 2 ways to find the square root of 53:
 Long Division Method
 Prime Factorization
Long Division Method
The square root of 53 by long division method consists of the following steps:
 Step 1: Starting from the right, we will pair up the digits 53 by putting a bar above 53. We also pair the 0s in decimals in pairs of 2 from left to right.
 Step 2: Find a number that, when multiplied to itself, gives a product less than or equal to 53. The number 7 fits here as 7 squares gives 49. Dividing 53 by 7 with quotient as 7, we get the remainder as 4.
 Step 3: Drag a pair of 0s down and fill it next to to make the dividend 400.
 Step 4: Double the divisor 7, and enter 14 below with a blank digit on its right. Think of a number which is greater than equal to dividend, i.e., 400. 142 is the perfect number to divide 400.
 Step 5: Multiply 142 by 2. 142 × 2 = 284 < 400 and write the remainder, i.e., 116.
 Step 6: Repeat this process until the quotient starts repeating after certain digit.
Therefore, the square root of 53 = 7.280
Prime Factorization
 To find the square root of 53, we shall first express it in terms of its prime factors.
Prime factorization of 53 = 1 × 53  Since all the prime factors of 53 are unique none of these factors are perfect squares, the square root of 53 cannot be simplified.
 Therefore, the Square Root of √53 = 7.280
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Challenging Questions
 What is the negative root of 5300?
 Find the square root of 5300 up to 5 decimal places?
 What is the square root of:
a) 530
b) 153
Solved Examples

Example 1: Rob is multiplying a number by itself. If the product is 53, help Rob in finding the number.
Solution:
To find the number let us assume number = y
On multiplying y times y = y × y = 53
y² = 53
y = √53
y = 7.280
(7.280 × 7.280 = 52.999 ≅ 53)
The number is 7.280. 
Example 2: The area of a squareshaped table is 2809 square units. Calculate the measurement of one side of the table.
Solution:
The area of table = 2809 sq. units
To find the side of the squareshaped table, let us take square root of 2809 by prime factorization method.
2809 = 1 × 53 × 53
Square root of 2809 is 53.
Therefore, side of square table is 53 units.
FAQs on Square Root of 53
What is the square root of 53 using prime factorization?
Prime factorization of 53 = 1 × 53
√53 = 7.280
Is 53 a perfect square root?
53 is not a perfect square. 53 is a natural number, but since there is no other natural number that can be squared to result in the number 53, it is NOT a perfect square.
What is the decimal value of the square root of 53?
The decimal value of the square root of 53 is √53 = 7.280.
Is the square root of 53 a rational number?
No, the square root of 53 is not a rational number since the square root of 53 is nonterminating and cannot be represented in the form of p/q.
Can we find the square root of 53 by the repeated subtraction method?
No, we can’t find the square root of 53 by repeated subtraction method as it can be used only for perfect squares. 53 is not a perfect square.