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

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Square root of 11: 3.3166247903554Square source of 11 in exponential form: (11)½ or (11)0.5Square root of 11 in radical form: √11
1.What Is the Square root of 11?
2.Is Square root of 11 Rational or Irrational?
3.How to find the Square source of 11?
4.FAQs top top Square root of 11

The square root is an station mathematical operation of a square. The square source of a number is the number the gets multiply to chin to give the product. Let"s take it a look at the below example: This is a number which once multiplied to itself gives us the an outcome as 11. The square root of 11 is represented as √11. The square source of 11 in the exponent form is expressed as 11½ . The square source of 11 rounded to 5 decimal locations is + 3.31662 and - 3.31662.

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

p and q are integersq ≠ 0

A number that cannot be expressed together a proportion of two integers is an irrational number. Non-terminating decimals having repeated numbers after the decimal point are reasonable numbers. Now let united state look in ~ the square root of 11

√11 = 3.31662479036

Do friend think the decimal component stops after ~ 3.31662479036? clearly No, this is non-terminating and also the decimal part has no repeating pattern. So it is not a rational number. Thus, √11 is one irrational number.

How to find the Square source of 11?

Square source of 11 can be calculated using assorted methods:

By simplifying the radical that the numbers that room perfect squares.By long division method for perfect and also non-perfect squares

11 is a prime number and hence, that is no a perfect square. 

Therefore, the square root of 11 have the right to only be found by the long department method.

Simplified Radical form of Square root of 11

To leveling the square source of 11, allow us first express 11 as a product of its element factors. The prime factorization of 11 can be uncovered as follows: for this reason the element factorization of 11 is: 1 × 11 To uncover the square root of any kind of number, we take one number from every pair of the very same numbers native its element factorization and also we multiply them. Yet the prime factorization that 11 is 11 × 11 which has no pairs of the very same numbers. Therefore, √11 is in the lowest kind and cannot be simplified further. Have the right to you shot and express the square source of 5 and the square source 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 is composed of the complying with steps:

Step 1: Starting indigenous the right, we will pair up the number by placing a bar above them.Step 2: uncover a number together that when you multiply it v itself, the product is much less than or same to 11. So, the number is 3. Putting the divisor as 3, we get the quotient as 3 and the remainder 2Step 3: twin the divisor and enter it v a blank on the right. Guess the largest feasible digit to fill the blank which will additionally become the brand-new digit in the quotient, such that as soon as the new divisor is multiplied to the new quotient the product is less than or equal to the dividend. Divide and also write the remainder. Repeat this procedure to gain the decimal locations you want.


Hence, √11 = 3.3166

Explore Square roots making use of illustrations and also interactive examples

Think Tank:

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

Important Notes:

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

Example 1: Jim had a doubt. He knew the 3.316 is the square source of 11. He wanted to recognize if -3.316 is also a square root of 11? can you clear up his doubt?


Let us take an instance of a perfect square number and extend the exact same logic to clarify her doubt. We understand that 4 is a square root of 16 because once 4 is multiplied to chin it provides 16 yet what about -4?Let us multiply and check (-4) × (-4) = 16, (-) × (-) = +Therefore, -4 is additionally a ssquare source of 16. Walk by the exact same logic, -3.316 is also a square source of 11.

Example 2: man is baking a square cake for his friend"s birthday party. That decides to provide each guest a square piece of cake of side 1inch. There room 121 guests attending the party. What need to be the length of the sides that his square cake so that he can serve every the guest 1 piece each?


Since there room 121 guests, the number of cake pieces must be 121. Since each piece of cake needs to be 1 inch by 1 inch, the area that the square cake should be 121 sq. Inches.Therefore, length of the political parties of the cake = 121 = √11Length the the sides of the square cake = 11 inches

Example: If the area the a one is 11π in2. Discover the radius the the circle.


Let "r" it is in the radius of the circle.⇒ Area the the one = πr2 = 11π in2⇒ r = ±√11 inSince radius can"t it is in negative,⇒ r = √11The square root of 11 is 3.317.⇒ r = 3.317 in

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FAQs on the Square root of 11

What is the worth of the Square root of 11?

The square root of 11 is 3.31662.

Why is the Square root of 11 an Irrational Number?

The number 11 is prime. This implies that the number 11 is pairless and also is not in the power of 2. Therefore, the square source of 11 is irrational.

What is the Square source of 11 in simplest Radical Form?

The number 11 is a prime number. This means that the number 11 is pairless and is no in the strength of 2. Therefore, the radical type of square source of 11 cannot be simplified further.

What is the Square root of -11?

The square root of -11 is an imaginary number. It have the right to be composed as √-11 = √-1 × √11 = i √11 = 3.316iwhere i = √-1 and also it is called the imaginary unit.

If the Square source of 11 is 3.317. Find the value of the Square root of 0.11.

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Let us represent √0.11 in p/q type i.e. √(11/100) = 0.11/10 = 0.332. Hence, the value of √0.11 = 0.332

What is the worth of 12 square root 11?

The square root of 11 is 3.317. Therefore, 12 √11 = 12 × 3.317 = 39.799.