127 LearnersLast updated on May 26th, 2025
Square Root of 1111
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 1111.
What is the Square Root of 1111?
The square root is the inverse of the square of the number. 1111 is not a perfect square. The square root of 1111 is expressed in both radical and exponential form. In the radical form, it is expressed as √1111, whereas (1111)^(1/2) in the exponential form. √1111 ≈ 33.3317, 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 1111
The prime factorization method is used for perfect square numbers. However, the prime factorization method is not used for non-perfect square numbers where 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 1111 by Prime Factorization Method
The product of prime factors is the prime factorization of a number. Now let us look at how 1111 is broken down into its prime factors.
Step 1: Finding the prime factors of 1111 Breaking it down, we get 11 × 101 as the prime factors of 1111.
Step 2: Now we found out the prime factors of 1111. The second step is to make pairs of those prime factors. Since 1111 is not a perfect square, the digits of the number can’t be grouped in pairs. Therefore, calculating 1111 using prime factorization is impossible.
Square Root of 1111 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 1111, we need to group it as 11 and 11.
Step 2: Now we need to find n whose square is 11. We can say n as ‘3’ because 3 × 3 is the closest to 11. Now the quotient is 3 and the remainder is 11 - 9 = 2.
Step 3: Bring down the next group of digits, which is 11, making it 211.
Step 4: Double the quotient and write it in the new divisor, which is 6.
Step 5: Append a digit x to 6 to get 6x, such that 6x × x is less than or equal to 211. Let x be 3, then 63 × 3 = 189.
Step 6: Subtract 189 from 211 to get a remainder of 22.
Step 7: Since the remainder is less than the divisor, add a decimal point and bring down two zeros to make it 2200.
Step 8: Double the previous quotient, which was 33, to get 66, and write it down.
Step 9: Repeat the steps to find the next digit. The process continues similarly to get more decimal places. So the square root of √1111 is approximately 33.33.
Square Root of 1111 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 1111 using the approximation method.
Step 1: Now we have to find the closest perfect squares of √1111. The smallest perfect square close to 1111 is 1024, and the largest perfect square is 1156. √1111 falls somewhere between 32 and 34.
Step 2: Now we need to apply the formula: (Given number - smallest perfect square) / (Greater perfect square - smallest perfect square). Using the formula (1111 - 1024) / (1156 - 1024) ≈ 0.6914. Adding this to the smaller perfect square root value, we get 32 + 0.6914 ≈ 32.69, so the square root of 1111 is approximately 33.33.
Common Mistakes and How to Avoid Them in the Square Root of 1111
Students do make mistakes while finding the square root, such as forgetting about the negative square root, skipping long division steps, etc. 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 most real-world applications.
For example: √1111 ≈ 33.33, but there is also -33.33 which should not be forgotten.
Mistake 2
Not adding 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.
For example: √(25 + 36) ≠ √25 + √36. The right way is √(25 + 36) = √61.
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 ≈ 7.071, not 7.
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, resulting in a wrong answer at the end of the sum. This may either happen in subtracting or elsewhere in the process.
Square Root of 1111 Examples
Problem 1
Can you help Alex find the area of a square box if its side length is given as √1111?
The area of the square is approximately 1234.4321 square units.
Explanation
The area of the square = side².
The side length is given as √1111.
Area of the square = (√1111)² = 1111.
Therefore, the area of the square box is approximately 1234.4321 square units.
Problem 2
A square-shaped building measuring 1111 square feet is built; if each of the sides is √1111, what will be the square feet of half of the building?
555.5 square feet
Explanation
We can just divide the given area by 2 as the building is square-shaped.
Dividing 1111 by 2 = we get 555.5.
So half of the building measures 555.5 square feet.
Problem 3
Calculate √1111 × 5.
Approximately 166.6585
Explanation
The first step is to find the square root of 1111, which is approximately 33.3317.
The second step is to multiply 33.3317 with 5.
So 33.3317 × 5 ≈ 166.6585.
Problem 4
What will be the square root of (1111 + 25)?
The square root is approximately 34.29.
Explanation
To find the square root, we need to find the sum of (1111 + 25). 1111 + 25 = 1136, and then √1136 ≈ 33.69. Therefore, the square root of (1111 + 25) is approximately ±33.69.
Problem 5
Find the perimeter of the rectangle if its length ‘l’ is √1111 units and the width ‘w’ is 35 units.
We find the perimeter of the rectangle as approximately 136.6634 units.
Explanation
Perimeter of the rectangle = 2 × (length + width).
Perimeter = 2 × (√1111 + 35) ≈ 2 × (33.3317 + 35) ≈ 136.6634 units.
FAQ on Square Root of 1111
1.What is √1111 in its simplest form?
2.Mention the factors of 1111.
3.Calculate the square of 1111.
4.Is 1111 a prime number?
5.1111 is divisible by?
6.How does learning Algebra help students in Singapore make better decisions in daily life?
7.How can cultural or local activities in Singapore support learning Algebra topics such as Square Root of 1111?
8.How do technology and digital tools in Singapore support learning Algebra and Square Root of 1111?
9.Does learning Algebra support future career opportunities for students in Singapore?
Important Glossaries for the Square Root of 1111
- Square root: A square root is the inverse of a square. Example: 4² = 16 and the inverse of the square is the square root, that 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.
- Principal square root: A number has both positive and negative square roots; however, it is always the positive square root that has more prominence due to its uses in the real world. That is why it is also known as the principal square root.
- Prime factorization: It is the process of expressing a number as a product of its prime factors.
- Long division: A method used to divide large numbers into simpler parts, often used to find square roots of non-perfect squares.
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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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