Square root of 39
2026-02-28 00:53 Diff
https://brightchamps.com/en-us/math/algebra/square-root-of-39

595 Learners

Last updated on August 5, 2025

Square root is a mathematical operation where a factor of a number is multiplied by itself, giving the original number. For financial estimations, geometry problems, the function of square root is used. In this topic, we will learn about the square root of 39.

What is the square root of 39?

The square root is the number that gives the original number when it is multiplied twice. √39 = 6.2449979984 in exponential form it is written as √39 =391/2. In this article we will learn more about the square root of 39, how to find it and common mistakes.
 

Finding the square root of 39

Students learn different methods to find out square roots. For a perfect square root, the process is simple. Here, it is noticed that 39 is not a perfect square. Few methods are explained below - 
 

Square Root of 39 By Prime Factorization

Prime factorization of 39:


39= 3×13


For finding square roots, prime factorization is a usual way. In this method, a number is expressed as a product of prime factors. The number cannot be expressed as a simple radical form, as it is an irrational number. 
 

Explore Our Programs

Square Root of 39 By Long division

For the division method, the number has to be in pairs from the right side. Firstly, the number has to be segmented into pairs from the right side of the number. If there is an odd count of digits, then that digit has to be kept as it is.

The division method starts from the leftmost side of the number. The closest square number to the first segment can be used as a divisor. In this case, 39 is in pairs therefore, the closest square number is 6. So the square root of the number lies between 6 and 7. 

Step 1: Pair 39 with zeros, as it has no decimals in it.


39.00→ (39)(00) 


Step 2: pick a number whose square is ≤ 39, 62=36


— 6 is the quotient. 


— Subtract the numbers, 39-36=2. 


Step 3: double quotient and use it as the first digit of the new divisor’s


— Double 6


— Now find the digit x in a way that 2x×x ≤ 300


— x is 2, 121×2 = 244.


Step 4: Now find the final quotient 


The result; √39 =  6.2449
 

Square Root of 39 By Approximation

In the approximation method, we estimate the square root by considering the closest perfect square to 39.


Follow the below steps; 


Step 1: Nearest perfect square to 39 → √36=6 and √49 = 7 


Step 2: The root of 39 will also be higher than 6 but lower than 7 because 39 is greater than 36 but lesser than 49.


Step 3: We try to test numbers like 6.1,6.08 and further. We find that √39 =  6.2449
 

Common Mistakes and How to Avoid Them in the Square Root of 39

Children learn square root in grade 6 or 7. It is quite usual to make mistakes while solving square root. Few mistakes are explained below - 
 

Download Worksheets

Problem 1

Solve for x in the equation x²−39=0.

Okay, lets begin

Start with the equation:


x2−39=0


Add 39 to both sides:


x2=39


Take the square root of both sides:


x=±√39 


Approximate the square root of 39:


x=±6.245
 

Explanation

The solutions are x=6.245 or x=−6.245.

Well explained 👍

Problem 2

A circle has an area of 39 square units. Find the radius of the circle.

Okay, lets begin

A=πr2


Substitute the given area A=39:


39=πr2


Solve for r2:


r2=39/π


Using π≈3.1416:


r2≈39/3.1416≈12.41


Take the square root of both sides:


r≈12.419≈3.524
 

Explanation

Thus, the radius of the circle is approximately r≈3.524 units.

Well explained 👍

Problem 3

Express 1/√39 ​in simplified radical form.

Okay, lets begin

 To simplify the expression 1/√39. Rationalize the denominator. We do this by multiplying the numerator and denominator with √39


1/√39×√39/√39=√39/39
 

Explanation

 Thus, the simplified form of 1/√39 is √39/39​​.

Well explained 👍

FAQs on 39 Square Root

1. Is √441 rational?

2.Is 117 a composite number?

— Yes. 117 has more than just 2 factors. It cannot be a prime number.

3. Is 53 a perfect square?

— The square root of 53 is a decimal number. We cannot assume it is a perfect square.  
 

4. Is 12 a perfect square?

— The square root of 12 is an irrational value. It is expressed in decimal form. It is not a perfect square. 
 

Important glossaries for the square root of 39

  • Integer — A number both positive and negative that lies between zero and infinity is called an integer.
  • Prime numbers —  A number that can be divisible only by 1 or the number itself is called a prime number.
  • Perfect square number — A number is called a perfect square when the root operation is applied, the answer comes out as a whole number.
  • Non-perfect square numbers —  A number is called a non-perfect square number, if the root operation is applied, the answer comes out as a fraction.

What Is Algebra? 🧮 | Simple Explanation with 🎯 Cool Examples for Kids | ✨BrightCHAMPS Math

▶

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.

Fun Fact

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