In this article, we will analyze and find the square root of 61 using various mathematical techniques and approximation methods.

The square root of the numeral 61 is 7.810.

The square root of a quantity can be defined as the quantity that, when doubled, produces a similar quantity that is similar in quantity to the square.

√61 = √(7.810 x 7.810).Note: Since the second input is a mathematical equation, it does not require any rewriting or synonym replacement.

√61 = √(7.810)$^2$.

The square root of 61 is approximately ±7.810.

Both negative and positive integers produce the square root. The square root of 61 is 7.810, thus obtaining it. Therefore, it is equivalent to 1/2 when canceled out with the square root.

## How To Calculate the Square Root of 61?

Two commonly employed techniques for calculating the square root of 61 are the Approximation technique and the Long Division method.

When the square root of any number is taken, it yields the actual value. The symbol √ is used to represent the square root.

Let’s explore each of them to gain a deeper understanding of the concepts.

### Square Root of 61 by Long Division Method

The long division process is one of the most commonly used methods to find the square roots of a given number. It reduces a multi-digit number to equal parts, providing more accurate and reliable answers. Additionally, it is easy to comprehend.

To perform the operations of addition, subtraction, multiplication, and division repeatedly, you will require all of them in primary five. Learning how to find the square root of a number is made easy with the method of long division.

Here are the simple guidelines that need to be followed in order to find the square root of 61 using the long division method:

### Step 1

Firstly, represent the given number 61 in the division symbol, as illustrated in figure 1.

### Step 2

Beginning from the right-hand side of the numeral, split the numeral 61 into pairs like 00 and 61.

### Step 3

The quotient in this case is 7, while the remainder is 12. Dividing the digit 61 by a number yields either 61 itself or a number smaller than 61.

### Step 4

After bringing down the next divisor, consider it as the divisor. Hence, when 14 is divided by 7, we need to double our obtained quotient. Now, the dividend is 12. After bringing down the next pair, consider it as the divisor.

### Step 5

If the number is not a perfect square, add a pair of zeros to the right of the number before dividing. Now, multiply the divisor with another number to make a new divisor that results in 12 or less when multiplied with 14.

### Step 6

1200 is less than 1184 in the results of dividing 148 by 8. By adding the divisor to 8, a remainder of 16 is obtained. The same process mentioned above should be repeated, and the next pair of zeros should be moved down.

### Step 7

Keep repeating the same steps until the remainder is zero, if the division process infinitely continues to obtain two decimal places.

### Step 8

The square root of 61 is 7.810, which is the end result. Figure 1 depicted underneath demonstrates the elaborate procedure of long division.

### Square Root by Approximation Method

The approximation method involves estimating the square root of a non-perfect square number by taking the average and dividing it by a perfect square number that is either smaller or larger than the given number.

The provided detailed instructions must be adhered to in order to calculate the square root of 61 using the approximation method.

### Step 1

Take into account a square number that is precisely 49 smaller than 61.

### Step 2

Now divide 61 by the square root of 49.

61 divided by 7 equals 8.71.

### Step 3

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(7 + 8.71) ÷ 2 = 7.85.

### Important points

## Is Square Root of 61 a Perfect Square?

Also, if a number is a perfect square, it is rational. A number is a perfect square if it can be divided into two equal parts or whole identical numbers. However, the number 61 is not a perfect square.

A rational number, denoted as a, is the square root of a perfect square a. Therefore, a rational number is expressed in the form q/p, where a is a natural number.

It can be proved below. It is not a perfect square, as far as 61 is concerned. It is a decimal number, and it is irrational as it is not a perfect square.

The factorization of 61 yields 1 multiplied by 61.

Calculating the square root of the expression mentioned above yields:

= √(1 x 61).Output: = √(1 multiplied by 61).

= (1 x 61)$^{1/2}$.Output: = (1 multiplied by 61)$^{1/2}$.

= 7.810.

This demonstrates that 61 is not a perfect square since it contains decimal points; therefore, it is an irrational number.