Square Root of 39
The square root of 39 is a number which when multiplied by itself, results in the number 39. 39 is an odd number. Let us determine the square root of 39 in this lesson. We will learn how to calculate the square root of 39 and find out whether the square root of 39 is rational or irrational. We will also look at a few problems to help us understand this topic better.
 Square Root of 39: √39 = 6.244
 Square of 39: 39^{2} = 1521
1.  What is the Square Root of 39? 
2.  Is Square Root of 39 Rational or Irrational? 
3.  How to Find the Square Root of 39? 
4.  Challenging Questions 
5.  FAQs on Square Root of 39 
What Is the Square Root of 39?
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: √39
 Decimal form: 6.244
 Exponent form: (39)^{1/2}
Is Square Root of 39 Rational or Irrational?
 39 is a number that is not a perfect square; this indicates that it does not have a natural number as its square root.
 Square root of 39 can be simplified in its decimal form to √39 = 6.244
 Square root of 39 cannot be expressed as a fraction of the form p/q which tells us that the square root of 39 is an irrational number.
How to Find the Square Root of 39?
There are 2 ways to find the square root of 39:
 Long Division Method
 Prime Factorization
Long Division Method
The square root of 39 by long division method consists of the following steps:
 Step 1: Starting from the right, we will pair up the digits 39 by putting a bar above 39. We will 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 39. The number 6 fits here as 6^{2} gives 36. Dividing 39 by 6 with quotient as 6, we get the remainder as 3.
 Step 3: Drag a pair of 0’s down and fill it next to 3 to make the dividend 300.
 Step 4: Double the divisor 6, and place 12 as the divisor with a blank digit on its right. Think of a number which is greater than or equal to the dividend, i.e. 300. 122 is the perfect number to divide 300.
 Step 5: Multiply 122 by 2. 122 × 2 = 244 < 300. Now write the remainder, i.e. 56.
 Step 6: Repeat this process until you get a required quotient.
Therefore, the square root of 39 = 6.244
Prime Factorization
 To find the square root of 39, we shall first express it in terms of its prime factors.
Prime factorization of 39 = 3 × 13  Since all the prime factors of 39 are unique, none of these factors are perfect squares. Thus, the square root of 39 cannot be simplified.
 Finding the root is very easy:
√39 = √(3 × 13)
√39 = 6.244
Therefore, the square root of 39 ≅ 6.244
Explore square roots using illustrations and interactive examples
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Challenging Questions
 What is the negative root of 3900?
 Find the square root of 3900 up to 5 decimal places?
 What is the square root of:
a) 3939
b) 139
Solved Examples

Example 1: Robert wants to buy a new wall painting. In the store, he finds a square painting that has an area of 1521 square units. How long is each side of the painting?
Solution:
To find the side of the painting, we will have to find the square root of 1521.
The square root is √1521 = 39.
Hence, the side length of the painting is approximately 39 units. 
Example 2: Find the square root of 39 up to 3 decimal places.
Solution:
Follow the below steps to find the square root of 39 up to 3 decimal places. Step 1: Starting from the right, we will pair up the digits 39 by putting a bar above 39. We will 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 39. The number 6 fits here as 62 gives 36. Dividing 39 by 6 with quotient as 6, we get the remainder as 3.
 Step 3: Drag a pair of 0’s down and fill it next to 3 to make the dividend 300.
 Step 4: Double the divisor 6, and enter 12 as the divisor with a blank digit on its right. Think of a number which is greater than or equal to the dividend, i.e. 300. 122 is the perfect number to divide 300.
 Step 5: Multiply 122 by 2. 122 × 2 = 244 < 300. Now write the remainder, i.e. 56.
 Step 6: Repeat this process until you get the required quotient.
Therefore, the square root of 39 up to 3 decimal places is 6.244.
FAQs on Square Root of 39
What is the square root of 39 using prime factorization?
Prime factorization of 39 = 3 × 13
√39 = √(3 × 13)
√39 = 6.244
Is 39 a perfect square root?
39 is not a perfect square. 39 is a natural number, but since there is no other natural number that can be squared to result in the number 39, it is NOT a perfect square.
What is the decimal value of the square root of 39?
The decimal value of the square root of 39 is √39 = 6.244.
Is the square root of 39 a rational number?
No, the square root of 39 is not a rational number since the square root of 39 is nonterminating and cannot be represented in the form of p/q.
Can we find the square root of 39 by the repeated subtraction method?
No, we can’t find the square root of 39 by repeated subtraction method as it can be used only for perfect squares. 39 is not a perfect square.
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