from a handpicked tutor in LIVE 1to1 classes
Square Root of 61
The square root of 61 is expressed as √61 in the radical form and as (61)^{½} or (61)^{0.5} in the exponent form. The square root of 61 rounded up to 7 decimal places is 7.8102497. It is the positive solution of the equation x^{2} = 61.
 Square Root of 61: 7.810249675906654
 Square Root of 61 in exponential form: (61)^{½} or (61)^{0.5}
 Square Root of 61 in radical form: √61
What Is the Square Root of 61?
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 nonsquare 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
Is the Square Root of 61 Rational or Irrational?
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 nonterminating (i.e it never ends) and nonrecurring (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 neverending and you cannot see a pattern in the decimal part. So √61 is an irrational number.
How to Find the Square Root of 61?
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 6149 = 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.
Important Notes:
 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
Challenging Questions:
 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.
Square Root of 61 Solved Examples

Example 1: Fredrick told his friends that the value of −√61 is same as √−61. What do you think?
Solution:
Negative square root cannot be a real number.
−√61 is a real number. But √−61 is an imaginary number. 
Example 2:Joel had a doubt. He knew that 7.8102 is the square root of 61. He wanted to know if −7.8102is also a square root of 61? Can you clarify his doubt?
Solution:
Let us take an example of a perfect square number and extend the same logic to clarify her doubt.
We know that 3 is a square root of 9 because when 3 is multiplied to itself, it gives 9.
But what about −3?Let us multiply and check.−3 ×−3=9∵(− × − = +)Therefore 3 is also a square root of 9.
Going by the same logic,−7.8102 is also the square root of 61. 
Example: If the area of a circle is 61π in^{2}. Find the radius of the circle.
Solution:
Let 'r' be the radius of the circle.
⇒ Area of the circle = πr^{2} = 61π in^{2}
⇒ r = ±√61 in
Since radius can't be negative,
⇒ r = √61
The square root of 61 is 7.810.
⇒ r = 7.810 in
FAQs on the Square Root of 61
What is the Value of the Square Root of 61?
The square root of 61 is 7.81024.
Why is the Square Root of 61 an Irrational Number?
The number 61 is prime. This implies that the number 61 is pairless and is not in the power of 2. Therefore, the square root of 61 is irrational.
What is the Square Root of 61 in Simplest Radical Form?
The number 61 is a prime number. This implies that the number 61 is pairless and is not in the power of 2. Therefore, the radical form of square root of 61 cannot be simplified further.
If the Square Root of 61 is 7.810. Find the Value of the Square Root of 0.61.
Let us represent √0.61 in p/q form i.e. √(61/100) = 0.61/10 = 0.781. Hence, the value of √0.61 = 0.781
What is the Value of 5 square root 61?
The square root of 61 is 7.810. Therefore, 5 √61 = 5 × 7.810 = 39.051.
Is the number 61 a Perfect Square?
The number 61 is prime. This implies that the square root of 61 cannot be expressed as a product of two equal integers. Therefore, the number 61 is not a perfect square.
visual curriculum