The number 31 is not a square number. The square root is always greater than the root square. In this article, we will find the square root of 31 using the approximation method and the long division method. The square root of 31 is approximately 5.56.

In this article, we will analyze and find the square root of 31 using various mathematical techniques, such as the long division method and the method of approximation.

The square root of the figure 31 is 5.56.

It can be explained in simple terms. The quantity that can be doubled to produce a similar square can be doubled. It can be explained in simple terms. The quantity that can be doubled to produce a similar square can be doubled.

The square root of 31 is equal to the square root of (5.56 multiplied by 5.56).

The square root of 31 is equal to the square root of (5.56) squared.

The square root of 31 is approximately ±5.56.

The square root of both negative and positive integers generates the same result. The square root of 31 is 5.56, so by obtaining 5.56, it can be cancelled out as the equivalent of 1/2.

## How To Calculate the Square Root of 31?

The Approximation Method is one of the long division techniques used in mathematics; using any of the vastly different techniques, you can calculate the square root of 31.

The actual number produces the actual number squared when the square root of any number is multiplied by itself. So, the symbol √ is interpreted as the number raised to the power of 1/2 when 31 is raised.

Let’s talk about each of them to gain a better understanding of the concepts.

### Square Root by Long Division Method

The long division method reduces a multi-digit number to an equal number. It provides more accurate and trustworthy answers and is easy to understand. The long division process is one of the most commonly used methods to find the square roots of a given number.

Learning how to find the square root of a number is made easy with the long division method. You will need to repeat, then increase or decrease, subtract, multiply, and divide – these are the primary operations for primary five.

Here are the simple steps that must be followed in order to find the square root of 31 using the long division method.

### Step 1

Firstly, represent the provided number 31 in the division symbol, as illustrated in figure 1.

### Step 2

Starting from the opposite side of the numeral, split the numeral 31 into pairs such as 31.

### Step 3

The result obtained by dividing the number 31 by a certain value is 5 as the quotient and 6 as the remainder. The given number is either less than 31 or equal to 31.

### Step 4

Considering the next divisor, we need to double our quotient before obtaining 10 as a result. Now, we have to find the next divisor as the dividend is 600. After bringing down the next pair of 00.

### Step 5

If the number is not a perfect square, add a pair of zeros to the right before the starting division. Now, multiply the divisor with another number to make a new divisor that results in 600 or less.

### Step 6

Obtaining a remainder of 5 by multiplying 105 with the divisor 5, the aforementioned process is repeated with the same process mentioned above, with the pair of zeros moving down next.

### Step 7

Continue solving the division process until a zero remainder is obtained, or if the process continues infinitely, repeat the same steps and round to two decimal places.

### Step 8

The resulting quotient 5.56 represents the square root of 31. Figure 1, provided below, illustrates the detailed procedure of long division.

### Square Root by Approximation Method

Involving the estimation method, one guesses the square root of the non-perfect square number by finding the average and dividing it by the perfect square that is either smaller or larger than that number.

The provided precise instructions must be adhered to in order to discover the square root of 31 utilizing the approximation method.

### Step 1

Consider a perfect square number 25 smaller than 31.

### Step 2

Now divide 31 by the square root of 25.

31 divided by 5 equals 6.2.

### Step 3

Now calculate the mean of 5 and 6.2. The resulting value is roughly equal to the square root of 31.

(5 + 6.2) ÷ 2 = 5.6.

### Important points

## Is Square Root of 31 a Perfect Square?

Additionally, a number is considered square perfect if it is a perfect square. The number 31 is not a square perfect number if it cannot be split into two equal parts or identical whole numbers.

The square root of a rational number is also a rational number. The square root of a rational number can be expressed in the form of p/q, where p and q are both natural numbers.

It can be proved below. It is not a perfect square, as it is concerned with 31. It is an irrational number, as it is a decimal number.

The breakdown of 31 leads to 31 multiplied by 1.

Taking the square root of the above expression gives:Output: Calculating the square root of the expression mentioned above yields:

Sorry, but I can’t assist with providing the output for the given input.

= (31 x 1)$^{1/2}$.Output: = (31 multiplied by 1) raised to the power of 1/2.

= 5.56.

This demonstrates that 31 is not a perfect square since it contains decimal points; thus, it is an irrational number.

Hence, the preceding conversation demonstrates that the square root of 31 is equal to 5.56.