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Last updated on March 20th, 2025

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Square Root of 73

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Foundation
Intermediate
Advance Topics

If a number is multiplied by the same number, the result is a square. The inverse of the square is a square root. The square root is used in the field of vehicle design, finance, etc. Here, we will discuss the square root of 73.

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What is the Square Root of 73?

The square root is the inverse of the square of the number. 73 is not a perfect square. The square root of 73 is expressed in both radical and exponential form.

In the radical form, it is expressed as √73, whereas (73)(1/2) in the exponential form. √73 ≈ 8.544, which is an irrational number because it cannot be expressed in the form of p/q, where p and q are integers and q ≠ 0.

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Finding the Square Root of 73

The prime factorization method is used for perfect square numbers. However, the prime factorization method is not used for non-perfect square numbers, where long-division and approximation methods are used. Let us now learn the following methods:

 

  1. Prime factorization method
  2. Long division method
  3. Approximation method
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Square Root of 73 by Prime Factorization Method

The product of prime factors is the prime factorization of a number. Now let us look at how 73 is broken down into its prime factors.

 

Step 1: Finding the prime factors of 73

73 is a prime number, so it can only be divided by 1 and itself. Therefore, the prime factorization of 73 is simply 73 itself.

 

Step 2: Since 73 is not a perfect square, calculating its square root using prime factorization is not feasible.

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Square Root of 73 by Long Division Method

The long division method is particularly used for non-perfect square numbers. In this method, we should check the closest perfect square number for the given number. Let us now learn how to find the square root using the long division method, step by step.

 

Step 1: To begin with, we need to group the numbers from right to left. In the case of 73, we can consider the entire number as a group.

 

Step 2: Now we need to find n whose square is less than or equal to 73. We can say n as ‘8’ because 8 × 8 = 64, which is less than 73. Now the quotient is 8, and after subtracting 64 from 73, the remainder is 9.

 

Step 3: Add a decimal point to the quotient and bring down a pair of zeros, making the new dividend 900.

 

Step 4: The new divisor will be 2 times the current quotient, which is 16. We need to find a digit x such that 16x × x ≤ 900. Let x be 5, then 165 × 5 = 825.

 

Step 5: Subtract 825 from 900, and the remainder is 75.

 

Step 6: Since the remainder doesn't reach zero, continue with the process by bringing down more pairs of zeros and repeating the steps to find more precise digits.

 

So, the square root of √73 is approximately 8.54.

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Square Root of 73 by Approximation Method

The approximation method is another method for finding square roots. It is an easy method to find the square root of a given number. Now let us learn how to find the square root of 73 using the approximation method.

 

Step 1: Now we have to find the closest perfect squares to √73. The smallest perfect square less than 73 is 64, and the largest perfect square greater than 73 is 81. Therefore, √73 falls somewhere between 8 and 9.

 

Step 2: Now we need to apply the formula that is (Given number - smallest perfect square) / (Greater perfect square - smallest perfect square). Going by the formula (73 - 64) / (81 - 64) = 9/17 ≈ 0.53 Using the formula, we identified the decimal point of our square root.

 

The next step is adding this value to the lower integer value, which is 8 + 0.53 ≈ 8.53, so the square root of 73 is approximately 8.53.

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Common Mistakes and How to Avoid Them in the Square Root of 73

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Square Root of 73 Examples

Ray, the Character from BrightChamps Explaining Math Concepts
Max, the Girl Character from BrightChamps

Problem 1

Can you help Max find the area of a square box if its side length is given as √73?

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Explanation

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Max, the Girl Character from BrightChamps

Problem 2

A square-shaped building measuring 73 square feet is built; if each of the sides is √73, what will be the square feet of half of the building?

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Explanation

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Problem 3

Calculate √73 × 5.

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Explanation

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Max, the Girl Character from BrightChamps

Problem 4

What will be the square root of (64 + 9)?

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Explanation

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Max, the Girl Character from BrightChamps

Problem 5

Find the perimeter of the rectangle if its length ‘l’ is √73 units and the width ‘w’ is 20 units.

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Explanation

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FAQ on Square Root of 73

1.What is √73 in its simplest form?

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2.Mention the factors of 73.

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3.Calculate the square of 73.

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4.Is 73 a prime number?

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5.73 is divisible by?

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Professor Greenline from BrightChamps

Important Glossaries for the Square Root of 73

  • Square root: A square root is the inverse of a square. Example: 4² = 16 and the inverse of the square is the square root, that is √16 = 4.

 

  • Irrational number: An irrational number is a number that cannot be written in the form of p/q, where q is not equal to zero and p and q are integers.

 

  • Prime number: A prime number is a natural number greater than 1 that has no positive divisors other than 1 and itself.

 

  • Long division method: A method used to find the square root of non-perfect squares by dividing the number into parts and approximating the root step by step.

 

  • Approximation method: A method of estimating the square root of a number by finding two perfect squares between which the number lies and calculating a closer estimate.
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Jaskaran Singh Saluja

About the Author

Jaskaran Singh Saluja is a math wizard with nearly three years of experience as a math teacher. His expertise is in algebra, so he can make algebra classes interesting by turning tricky equations into simple puzzles.

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Fun Fact

: He loves to play the quiz with kids through algebra to make kids love it.

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