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 =39^1/2. In this article we will learn more about the square root of 39, how to find it and common mistakes.
 

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 - 
 

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. 
 

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
 

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
 

• 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.