Estimate Square Root Of 11

Square Root of 11

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

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

1.	What Is the Square Root of 11?
two.	Is Square Root of 11 Rational or Irrational?
3.	How to Find the Square Root of eleven?
4.	FAQs on Square Root of eleven

What Is the Square Root of 11?

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

Is the Square Root of xi Rational or Irrational?

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 every bit a ratio of 2 integers is an irrational number. Non-terminating decimals having repeated numbers after the decimal point are rational numbers. Now allow us look at the square root of 11

√xi = 3.31662479036

Practice y'all think the decimal part stops later 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.

How to Find the Square Root of 11?

Square Root of 11 can be calculated using various methods:

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

xi is a prime and hence, it is not a perfect square.

Therefore, the square root of eleven tin only be found by the long division method.

Simplified Radical Class of Square Root of eleven

To simplify the square root of 11, allow u.s.a. offset express 11 as a production of its prime factors. The prime factorization of eleven tin be plant equally follows: Thus the prime number factorization of xi is: i × 11 To find the square root of any number, nosotros have one number from each pair of the same numbers from its prime factorization and we multiply them. But the prime factorization of 11 is xi × eleven which has no pairs of the same numbers. Therefore, √11 is in the lowest grade and cannot exist simplified further. Can you lot try and express the square root of 5 and the square root of 10 in a similar way?

Square Root of eleven By Long Division

The value of the square root of 11 by long sectionalisation method consists of the following steps:

Step 1: Starting from the right, we will pair upwards the digits by putting a bar in a higher place them.
Step 2: Find a number such that when you multiply it with itself, the production is less than or equal to eleven. Then, the number is three. Putting the divisor equally 3, we go the quotient as three and the remainder 2
Step 3: Double the divisor and enter information technology with a blank on its right. Guess the largest possible digit to fill the bare which will also get the new digit in the quotient, such that when the new divisor is multiplied to the new caliber the production is less than or equal to the dividend. Divide and write the remainder. Echo this process to go the decimal places you desire.

Finding the value of square root 11 using long division.

Hence, √11 = three.3166

Explore Square roots using illustrations and interactive examples

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Call back Tank:

Can y'all think of whatsoever quadratic equation which has a root every bit √xi?
Is √-11 a real number?
Since (-√11)²= xi, can we say that -√11 is also a square root of 11?

Important Notes:

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

Square Root of xi Solved Examples

Case 1: Jim had a dubiety. He knew that 3.316 is the square root of eleven. He wanted to know if -iii.316 is too a square root of 11? Can you clarify his dubiety?

Solution

Let united states take an case of a perfect square number and extend the same logic to clarify her doubt. We know that 4 is a foursquare root of 16 because when 4 is multiplied to itself information technology gives 16 Merely what virtually -4?
Let us multiply and check (-4) × (-4) = xvi, (-) × (-) = +
Therefore, -4 is also a ssquare root of 16. Going by the same logic,-3.316 is also a square root of 11.
Example 2: John is baking a foursquare cake for his friend's birthday party. He decides to requite each guest a square slice of cake of side 1inch. At that place are 121 guests attending the party. What should be the length of the sides of his square block so that he tin serve all the guests ane piece each?

Solution

Since there are 121 guests, the number of block pieces should be 121. Since each piece of block has to exist 1 inch past one inch, the area of the square cake should exist 121 sq. inches.
Therefore, length of the sides of the cake = 121 = √xi
Length of the sides of the square cake = 11 inches
Example: If the surface area of a circumvolve is 11π in². Find the radius of the circle.

Solution:

Let 'r' be the radius of the circumvolve.
⇒ Area of the circle = πr² = 11π in^two
⇒ r = ±√11 in
Since radius tin can't be negative,
⇒ r = √xi
The foursquare root of eleven is 3.317.
⇒ r = 3.317 in

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FAQs on the Foursquare Root of eleven

What is the Value of the Square Root of xi?

The square root of 11 is iii.31662.

Why is the Foursquare Root of 11 an Irrational Number?

The number 11 is prime. This implies that the number 11 is pairless and is non in the power of 2. Therefore, the square root of 11 is irrational.

What is the Foursquare Root of 11 in Simplest Radical Form?

The number 11 is a prime number. This implies that the number eleven is pairless and is not in the power of 2. Therefore, the radical class of square root of 11 cannot be simplified further.

What is the Square Root of -11?

The square root of -xi is an imaginary number. It tin be written every bit √-11 = √-1 × √eleven = i √11 = 3.316i
where i = √-1 and it is called the imaginary unit.

If the Square Root of 11 is 3.317. Discover the Value of the Square Root of 0.11.

Let us represent √0.11 in p/q form i.e. √(xi/100) = 0.11/10 = 0.332. Hence, the value of √0.xi = 0.332

What is the Value of 12 square root 11?

The foursquare root of 11 is 3.317. Therefore, 12 √xi = 12 × three.317 = 39.799.