Square root of 83
2026-02-28 21:32 Diff
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Last updated on October 23, 2025

When someone asks you to explain a square root, you can just tell that it is a number when multiplied by itself produces the same number. As we continue with our explanation, let’s assume the value of 83 Here 83 is considered as a non-perfect square root since it contain either decimal or fraction. Let's learn more about square roots in this article.

What is the square root of 83?

The square root of 83 can be easily found out by using long division method. In which it is discovered that the cumulative approximation of √83 is 9.110.
 

Finding the square root of 83.

There are many ways through which students can find square roots, and some of these methods are very popular. Some of the methods have been explained in detail below.
 

Square root of 83 using the prime factorization method.

In this method, we decompose the number into its prime factors.


Prime factorization of 83: 83 = 1×83


Since not all prime factors can be paired, 83 cannot be simplified into a perfect square. Therefore, the square root of 83 cannot be expressed in a simple radical form.

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Square root of 83 using the division method.

For non-perfect squares, we often use the nearest perfect square to estimate the square root. Follow these steps:


Step 1: Write the number 83 to perform long division.


Step 2: Identify a perfect square number that is less than or equal to 83. For 83, that number is 64 (8²).


Step 3: Divide 83 by 8. The remainder will be 19, and the quotient will be 10.


Step 4: Bring down the remainder (19) and append two zeros. Add a decimal point to the quotient, making it 10.0.


Step 5: Double the quotient to use as the new divisor, which gives 20.


Step 6: Select a number that, when multiplied by the new divisor, results in a product less than or equal to 1900.


Step 7: Continue the division process to find √83 to the desired decimal places. → √83 ≈ 9.110.

Square root of 83 using the approximation method

In the approximation method, we estimate the square root by identifying the closest perfect squares surrounding the number.


Step 1: The nearest perfect squares to 83 are √100 = 10 and √81 = 9.


Step 2: Since 83 is between 100 and 81, we know the square root will be between 10 and 9.


Step 3: By testing numbers like 9.1, 9.2 and further, we find that √83 ≈ 9.110.
 

Common mistakes when finding the square root of 83.

Here are some common mistakes students should avoid while learning to calculate the square root of 83.
 

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Problem 1

What is the square root of 0?

Okay, lets begin

→The square root of 0 is 0.
 

Explanation

Since 0×0=0 the square root of 0 is 0.
 

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Problem 2

Is √81 greater than 9.

Okay, lets begin

√81 = 9
 

Explanation

 Since 81 is a perfect square, √81 = 9, which is equal to 9 not greater than 9.
 

Well explained 👍

Problem 3

How do you find the square root of a non-perfect square, such as √18?

Okay, lets begin

→ √18


√18 = 3√2
 

Explanation

18 can be factored as 9×2 and 9 can be further factorized to 3 hence the final answer would be 3√2.
 

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FAQs on the square root of 83

1. Is 83 a prime number?

Yes, If we use long division on 83 we get to know that it has only two divisors which are 1 and itself, so it is a prime number. 
 

2. How do you simplify 8√80?

 8√80 can be simplified to 32√5, as we can express √80 as 4√5. 8 × 4 is equal to 32 hence it will be written as 32√5.
 

3.What is the difference between square root and cube root?

 A square root of a number is a value that, when multiplied by itself, gives that number. The cube root is a value that, when multiplied by itself twice, then the result is the said number.
 

4.What is the square root of 49?

 By applying the long division method on 49 we get to know that 7 divides 49 to 0 using 7 meaning 7 × 7 is equal to 49, which makes 7 the square root of 49.
 

5.What is the prime factorization of 83?

Using the prime factorization method, we can easily find out that 83 can be written as multiples of 1 and 83 to be more specific 83=1×83. Since it is a prime number.
 

  • Square Root: A number which when is multiplied by itself gives the original number is called a square root.
  • Perfect Square: A number that is the integral square of an integer I such that n = I², example I = 1, 2, 3, n = 1, 4, 9, 16, etc.
  • Prime Factorization: The ability to factorize a number in to the product of the basic arithmetic numbers, also known as primary numbers.
  • Non-Perfect Square: A figure that cannot be converted into an integer figure once divided by itself (e.g., 76).
  • Approximation Method: Approximating square root, that is, finding the closest integer which, when squared, yields the number being approximated.

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