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

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

• 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.

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

Explore square roots using illustrations and interactive examples

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• 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