122 LearnersLast updated on May 26th, 2025
Square Root of 11016
If a number is multiplied by the same number, the result is a square. The inverse of the square is a square root. The square root is used in various fields such as vehicle design, finance, etc. Here, we will discuss the square root of 11016.
What is the Square Root of 11016?
The square root is the inverse of the square of a number. 11016 is not a perfect square. The square root of 11016 is expressed in both radical and exponential form. In the radical form, it is expressed as √11016, whereas (11016)^(1/2) in the exponential form. √11016 ≈ 104.941, which is an irrational number because it cannot be expressed in the form of p/q, where p and q are integers and q ≠ 0.
Finding the Square Root of 11016
The prime factorization method is used for perfect square numbers. However, for non-perfect square numbers, the prime factorization method is not used; instead, the long-division method and approximation method are used. Let us now learn the following methods:
- Prime factorization method
- Long division method
- Approximation method
Square Root of 11016 by Prime Factorization Method
The product of prime factors is the prime factorization of a number. Now let us look at how 11016 is broken down into its prime factors.
Step 1: Finding the prime factors of 11016
Breaking it down, we get 2 × 2 × 2 × 3 × 3 × 3 × 3 × 17: 2^3 × 3^4 × 17
Step 2: Now we found out the prime factors of 11016. The second step is to make pairs of those prime factors. Since 11016 is not a perfect square, the digits of the number can’t be grouped in pairs completely. Therefore, calculating 11016 using prime factorization directly is not possible.
Square Root of 11016 by Long Division Method
The long division method is particularly used for non-perfect square numbers. In this method, we should check the closest perfect square number for the given number. Let us now learn how to find the square root using the long-division method, step by step.
Step 1: To begin with, we need to group the numbers from right to left. In the case of 11016, we need to group it as 16 and 110.
Step 2: Now we need to find n whose square is less than or equal to 110. We can say n as ‘10’ because 10^2 = 100 is lesser than or equal to 110. Now the quotient is 10 after subtracting 110 - 100, the remainder is 10.
Step 3: Now let us bring down 16, which is the new dividend. Add the old divisor with the same number: 10 + 10 = 20, which will be our new divisor.
Step 4: The new divisor will be 20n. We need to find the value of n that satisfies 20n × n ≤ 1016. Let us consider n as 5; now 205 × 5 = 1025.
Step 5: Subtract 1016 from 1025, the difference is -9. As it went negative, we take n as 4, now 204 × 4 = 816.
Step 6: Subtract 1016 from 816, the difference is 200, and the quotient becomes 104.
Step 7: Since the dividend is less than the divisor, we need to add a decimal point. Adding the decimal point allows us to add two zeroes to the dividend. Now the new dividend is 20000.
Step 8: Now we need to find the new divisor, which is 1049, because 1049 × 9 = 9441.
Step 9: Subtracting 9441 from 20000, we get the result 10559.
Step 10: Continue repeating these steps until we get two numbers after the decimal point or a suitable approximation.
So the square root of √11016 is approximately 104.941.
Square Root of 11016 by Approximation Method
The approximation method is another method for finding square roots. It is an easy method to find the square root of a given number. Now let us learn how to find the square root of 11016 using the approximation method.
Step 1: Now we have to find the closest perfect squares around √11016. The smallest perfect square less than 11016 is 10404 and the largest perfect square greater than 11016 is 11236. √11016 falls somewhere between 102 and 106.
Step 2: Now we need to apply the interpolation formula: (Given number - smallest perfect square) ÷ (Greater perfect square - smallest perfect square). Applying this formula, (11016 - 10404) ÷ (11236 - 10404) = 0.612.
Using the formula, we identified the decimal point of our square root. The next step is adding the value we got initially to the decimal number which is 104 + 0.612 = 104.612, so the square root of 11016 is approximately 104.612.
Common Mistakes and How to Avoid Them in the Square Root of 11016
Students do make mistakes while finding square roots, such as forgetting about the negative square root or skipping the long division method. Now let us look at a few of those mistakes that students tend to make in detail.
Mistake 1
Forgetting about the negative square root
It is important to make students aware that a number does have both positive and negative square roots. However, we will be taking only the positive square root, as it is the required one.
For example: √11016 ≈ 104.941, there is also -104.941 which should not be forgotten.
Mistake 2
Not adding the square root symbol in proper places
Not using the square root properly is another mistake that children make. To resolve this, we need to teach children that simplifying the numbers inside the square root is important and then move on to the second step.
For example: √(12+24) = √12 + √24 is the wrong method of using roots. The right way of using roots is √(12+24) = √36.
Mistake 3
Not finding the correct value of a non-perfect square
The first step that needs to be taught to children is to simplify the numbers inside the square root. This is important so that students do not make mistakes while identifying the approximate value.
For example: √50 = 7 is wrong, the correct answer is √50 ≈ 7.071.
Mistake 4
Confusing the square root symbol with the cube root
Students need to be taught the difference between cube root and square root constantly, as this will help them avoid mistakes.
For example: √50 and ∛50 are different.
Mistake 5
Making mistakes in long division
Finding a square root using the long division method involves many steps. Due to this, many students might skip a step accidentally, which results in a wrong answer at the end of the process. This may either happen in subtraction or elsewhere.
Square Root of 11016 Examples
Problem 1
Can you help Max find the area of a square box if its side length is given as √11016?
The area of the square is approximately 11016 square units.
Explanation
The area of the square = side².
The side length is given as √11016.
Area of the square = side² = (√11016)² = 11016.
Therefore, the area of the square box is approximately 11016 square units.
Problem 2
A square-shaped building measuring 11016 square feet is built; if each of the sides is √11016, what will be the square feet of half of the building?
5508 square feet
Explanation
We can just divide the given area by 2 as the building is square-shaped.
Dividing 11016 by 2 = we get 5508.
So half of the building measures 5508 square feet.
Problem 3
Calculate √11016 × 5.
Approximately 524.705
Explanation
The first step is to find the square root of 11016 which is approximately 104.941, the second step is to multiply 104.941 by 5.
So 104.941 × 5 ≈ 524.705
Problem 4
What will be the square root of (11016 + 64)?
The square root is approximately 104.687
Explanation
To find the square root, we need to find the sum of (11016 + 64). 11016 + 64 = 11080, and then √11080 ≈ 104.687.
Therefore, the square root of (11016 + 64) is approximately ±104.687.
Problem 5
Find the perimeter of the rectangle if its length ‘l’ is √11016 units and the width ‘w’ is 38 units.
We find the perimeter of the rectangle as approximately 285.882 units.
Explanation
Perimeter of the rectangle = 2 × (length + width).
Perimeter = 2 × (√11016 + 38) ≈ 2 × (104.941 + 38) ≈ 2 × 142.941 ≈ 285.882 units.
FAQ on Square Root of 11016
1.What is √11016 in its simplest form?
2.Mention the factors of 11016.
3.Calculate the square of 11016.
4.Is 11016 a prime number?
5.11016 is divisible by?
6.How does learning Algebra help students in United States make better decisions in daily life?
7.How can cultural or local activities in United States support learning Algebra topics such as Square Root of 11016?
8.How do technology and digital tools in United States support learning Algebra and Square Root of 11016?
9.Does learning Algebra support future career opportunities for students in United States?
Important Glossaries for the Square Root of 11016
- Square root: A square root is the inverse of a square. For example, 4^2 = 16 and the inverse of the square is the square root, which is √16 = 4.
- Irrational number: An irrational number is a number that cannot be written in the form of p/q, where q is not equal to zero and p and q are integers.
- Perfect square: A perfect square is a number that can be expressed as the product of an integer with itself. For example, 36 is a perfect square because 6 × 6 = 36.
- Long Division Method: A technique used to find the square root of non-perfect squares by dividing the number into groups and finding the square root step by step.
- Approximation Method: A method to estimate the square root of a number by finding the closest perfect squares and using interpolation to find an approximate value.
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Jaskaran Singh Saluja
About the Author
Jaskaran Singh Saluja is a math wizard with nearly three years of experience as a math teacher. His expertise is in algebra, so he can make algebra classes interesting by turning tricky equations into simple puzzles.
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