Square Root of 11 is approximately equal to 3.31662479. Here, as we know the square root of an integer is the value that returns the original number when multiplied by itself. Hence, √11 will result in the number 11. There are two possible square roots of 11 +3.3166… and -3.3166…

What is Square Root of 11?

Square Root of 11 up to 50 decimals is approximately

√11 = 3.3166247903553998491149327366706844953163631332646

The value of the square root of 11 is widely accepted as 3.316. The reason for this is that it contains an infinite number of decimals and to make mathematical computations easy, we use only 3 digits after decimal places. We can represent square root of 11 in the following two forms

• Fractional Exponent form: 11^1/2 = 3.316
• Radical Form: √11 = 3.316

Square Root of 11 Calculator

Try out the following calculator to calculate square root of 11

How to Find the Square Root of 11?

A square Root of 11 can be calculated using the following methods:

• Square Root by Long Division Method
• Estimation Method

Square Root of 11 by Long Division

To compute the square root of a non-perfect square, we need to perform the long division method. As 11 is also non- perfect square we use the Long Division method to find its square root.

Step 1: Write 11 as 11.000000 to make it easier to divide

Step 2: Now look for the perfect square less than 11 i.e. 3 and divide the number with it.

Step 3: Since the divisor is 3, the quotient is 3

Step 4: Subtract the square of 3 (which is 9) from 11, which gives us 2. Place a decimal in the quotient and bring down the pair of zeroes for further division.

Step 5: Now add the quotient with the existing divisor, this will become the digit at the tens place for our next divisor. For the unit’s place, we need to find a value that can be placed at the unit place of both the quotient and the divisor such that the new divisor when multiplied with the unit digit of the quotient results in the highest number less than the remainder.

Step 6: Now bring down the next pair of zeros and repeat the steps 4th and 5th. This can be done for infinite steps as the exact value of the square root of 11 goes up to infinite decimal places.

Square Root of 11 by Estimation Method

• Step 1: Let’s begin with the number 11.
• Step 2: Now, let’s use the square function to determine whether the guess is too big or too small. Thus, 3² = 9 it’s small.
• Step 3: So, Let’s take 3.2 because 3 is too small.
• Step 4: Again, use the square function to determine whether the guess is closer to the actual value. Thus, 3.2² = 10.24.
• Step 5: If 3.2 is still small, we have to continue with the same process.
• Step 6: Hence by following these steps we can guess the square root of 11.

Is Root 11 Rational or Irrational?

We have learnt that square root value of 11 is 3.31662… The decimal expansion of square root of 11 is non-terminating and non-repeating and we know that a non-terminating and non-repeating decimal expansion is an Irrational Number. Hence Square Root of 11 is irrational.

Also, Check

• Square Root of 10
• Square Root of 9
• Square Root of 8

Square Root of 11 Value – FAQs

What is Value of Square Root of 11?

The value of square root of 11 is approximately equal to 3.31662479

Is 11 a Prime Number?

Yes 11 is a prime number. It is only divisible by 1 and 11

Why is Square Root of 11 an Irrational Number?

The square root of 11 is considered an irrational number because it cannot be expressed as a simple fraction or ratio of two integers.

Is 11 a Perfect Square?

No 11 is not a perfect Square because its square root is not an integer

Does Square Root of 11 has Negative Value?

Yes, square root of 11 can take negative values as negative number when multiplied by itself results in positive