Square root of 61

Let us discover interesting facts about them. 61 is a prime prime. It is a twin prime with 59. It is the sum of squares of 2 numbers, 5² + 6² = 61. In this mini-lesson, we will learn about the square root of 61 by understanding methods to calculate the square root, the long division method to find the square root of any number, and how to apply them while solving problems.

• Square Root of 61: √61 = 7.81024
• Square of 61: 61² = 3721

The square root of a number is the number that gets multiplied to itself to give the product as the original number. The perfect square numbers like 9, 16, 25 and many more have square roots. The non-square numbers also have a square root, just that they are not whole numbers. 

• Square root of 61 in the radical form is expressed as √61 and in the exponent form it is expressed as 61^1/2.
• The square root of 61 rounded to 5 decimal places is + 7.81024 or - 7.81024

A number that cannot be expressed as a ratio of two integers is an irrational number. The decimal form of the irrational number will be non-terminating (i.e it never ends) and non-recurring (i.e the decimal part of the number never repeats a pattern). Now let us look at the square root of 61.  √61 = 7.81024967591

Do you think the decimal part stops after 7.81024967591? No, it is never-ending and you cannot see a pattern in the decimal part. So √61 is an irrational number.

We can find √61 using the method of approximation or using long division method.

Square Root of 61 by Long Division Method

The long division method helps us to find the accurate value of the square root of any number. The value of the square root of 61 by the long division method consists of the following steps:

• Step 1: Starting from the right, we will pair up the digits by putting a bar above them.
• Step 2: Find a number such that when you multiply it with itself, the product is less than or equal to 61. So, the number is 7. Putting the divisor as 7, we get the quotient as 7 and the remainder 61-49 = 12.
• Step 3: Double the divisor and enter it with a blank on its right. Guess the largest possible digit to fill the blank, which will also become the new digit in the quotient, such that when the new divisor is multiplied to the new quotient the product is less than or equal to the dividend. Divide and write the remainder. Repeat this process to get the decimal places you want.

Explore Square roots using illustrations and interactive examples.

• Square root of 63
• Square root of 98
• Square root of 56
• Square root of 16
• Square root of 41

• The square root of 61 in the radical form is expressed as √61.
• In exponent form square root of 61 is expressed as 61^1/2.
• The real roots of √61 are ±7.8102

• What is the value of -√√61?
• Simplify √61 × √61
• Determine the square root of 611 using the long division method up to 7 decimal places.

What is the square root of 61 in radical form?

The square root of 60 in the simplest radical form is √61.

Is square root of 61 a rational number?

The square root of 60 is not a rational number because we can not express√61 in the form of p/q  due to its non-terminating and non-repeating nature of decimal form. √61 is irrational.

What is the square of 61?

The square of 61 is 61 × 61 = 3721.

How do you find the square root of 61?

The best methods to find the square root of 61 are the approximation mehtod and the long division method.

What is the square root of √61 rounded to the nearest tenth?

The square root  of 61 to the nearest tenth is 7.8