Square Root of 11

The square root of 11 is expressed as √11 in the radical form and as (11)^½ or (11)^0.5 in the exponent form. The square root of 11 rounded up to 7 decimal places is 3.3166248. It is the positive solution of the equation x² = 11.

• Square Root of 11: 3.3166247903554
• Square Root of 11 in exponential form: (11)^½ or (11)^0.5
• Square Root of 11 in radical form: √11

The square root is an inverse mathematical operation of a square. The square root of a number is the number that gets multiplied to itself to give the product. Let's take a look at the below example: This is a number which when multiplied to itself gives us the result as 11. The square root of 11 is represented as √11. The square root of 11 in the exponent form is expressed as 11^½ . The square root of 11 rounded to 5 decimal places is + 3.31662 and - 3.31662.

A rational number is a number that is of the form p/q where:

• p and q are integers
• q ≠ 0

A number that cannot be expressed as a ratio of two integers is an irrational number. Non-terminating decimals having repeated numbers after the decimal point are rational numbers. Now let us look at the square root of 11

• √11 = 3.31662479036

Do you think the decimal part stops after 3.31662479036? Clearly No, this is non-terminating and the decimal part has no repeating pattern. So it is not a rational number. Thus, √11 is an irrational number.

Square Root of 11 can be calculated using various methods:

• By simplifying the radical of the numbers that are perfect squares.
• By long division method for perfect and non-perfect squares

11 is a prime number and hence, it is not a perfect square. 

Therefore, the square root of 11 can only be found by the long division method.

Simplified Radical Form of Square Root of 11

To simplify the square root of 11,  let us first express 11 as a product of its prime factors. The prime factorization of 11 can be found as follows: Thus the prime factorization of 11 is: 1 × 11 To find the square root of any number, we take one number from each pair of the same numbers from its prime factorization and we multiply them. But the prime factorization of 11 is 11 × 11 which has no pairs of the same numbers. Therefore, √11 is in the lowest form and cannot be simplified further. Can you try and express the square root of 5 and the square root of 10 in a similar way?

Square Root of 11 By Long Division

The value of the square root of 11 by 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 11. So, the number is 3. Putting the divisor as 3, we get the quotient as 3 and the remainder 2
• 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.

Hence, √11 = 3.3166

Explore Square roots using illustrations and interactive examples

• Square Root of 25
• Square Root of 30
• Square Root of 5
• Square Root of 250
• Square Root of 65

• Can you think of any quadratic equation which has a root as √11?
• Is √-11 a real number?
• Since (-√11)² = 11, can we say that -√11 is also a square root of 11?

• The real roots of √11 are ± 3.316.
• Irrational numbers cannot be expressed as a ratio of two integers. Example: π, √2.