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: 39² = 1521

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

• 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.

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 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 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

• Square Root of 45
• Square Root of 36
• Square Root of 29
• Square Root of 32
• Square Root of 34
• Square Root of 44
• Square Root of 27
• Square Root of 35 

• 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

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 non-terminating 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.