124 LearnersLast updated on May 26th, 2025
Square Root of 1121
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 fields like vehicle design, finance, etc. Here, we will discuss the square root of 1121.
What is the Square Root of 1121?
The square root is the inverse of the square of the number. 1121 is not a perfect square. The square root of 1121 is expressed in both radical and exponential forms. In the radical form, it is expressed as √1121, whereas (1121)^(1/2) in the exponential form. √1121 ≈ 33.487, 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 1121
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 and approximation methods are used. Let us now learn the following methods:
- Prime factorization method
- Long division method
- Approximation method
Square Root of 1121 by Prime Factorization Method
The product of prime factors is the prime factorization of a number. Now let us look at how 1121 is broken down into its prime factors.
Step 1: Finding the prime factors of 1121 Breaking it down, we find 1121 = 29 x 37.
Step 2: Now we have found the prime factors of 1121. Since 1121 is not a perfect square, the digits of the number can’t be grouped in pairs. Therefore, calculating 1121 using prime factorization is not straightforward.
Square Root of 1121 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 1121, we need to group it as 21 and 11.
Step 2: Now we need to find n whose square is less than or equal to 11. We can say n as '3' because 3 x 3 = 9 is less than 11. Now the quotient is 3, and after subtracting 9 from 11, the remainder is 2.
Step 3: Now let us bring down 21, which is the new dividend. Add the old divisor with the same number: 3 + 3 = 6, which will be our new divisor.
Step 4: The new divisor will be the sum of the dividend and quotient. Now we get 6n as the new divisor, and we need to find the value of n.
Step 5: The next step is finding 6n × n ≤ 221. Let's consider n as 3. Now, 63 x 3 = 189.
Step 6: Subtract 189 from 221; the difference is 32, and the quotient is 33.
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 3200.
Step 8: Now we need to find the new divisor and quotient. Using approximation, we get 334 x 4 = 1336.
Step 9: Subtracting 1336 from 3200, we get the result 1864.
Step 10: Now the quotient is 33.4.
Step 11: Continue doing these steps until we get two decimal places. So the approximate square root of √1121 is 33.487.
Square Root of 1121 by Approximation Method
The approximation method is another method for finding square roots, and 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 1121 using the approximation method.
Step 1: Now we have to find the closest perfect square to √1121. The smallest perfect square close to 1121 is 1024 (32^2), and the largest perfect square close to 1121 is 1156 (34^2). √1121 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). Applying the formula (1121 - 1024) / (1156 - 1024) = 97 / 132 ≈ 0.735. 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: 32 + 0.735 = 32.735. So the approximate square root of 1121 is 33.487.
Common Mistakes and How to Avoid Them in the Square Root of 1121
Students often make mistakes while finding the square root, such as forgetting about the negative square root or skipping long division steps. Let's look at a few of these mistakes in detail.
Mistake 1
Forgetting about the negative square root
It is important to make students aware that a number has both positive and negative square roots. However, we usually consider only the positive square root, as it is most often required.
For example: √50 ≈ 7.07, but there is also -7.07 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 students make. To resolve this, we need to teach students that simplifying the numbers inside the square root is important before moving to the next step.
For example: √(12+24) ≠ √12 + √24. The correct way 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 students 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, the correct answer is √50 ≈ 7.071067.
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. This may happen in subtracting or elsewhere.
Square root of 1121 Examples
Problem 1
Can you help Max find the area of a square box if its side length is given as √1121?
The area of the square is 1257.44 square units.
Explanation
The area of the square = side^2.
The side length is given as √1121.
Area of the square = side^2 = √1121 x √1121 = 33.487 × 33.487 ≈ 1257.44.
Therefore, the area of the square box is approximately 1257.44 square units.
Problem 2
A square-shaped building measuring 1121 square feet is built; if each of the sides is √1121, what will be the square feet of half of the building?
560.5 square feet
Explanation
We can just divide the given area by 2 as the building is square-shaped.
Dividing 1121 by 2, we get 560.5.
So half of the building measures 560.5 square feet.
Problem 3
Calculate √1121 x 5.
167.435
Explanation
The first step is to find the square root of 1121, which is approximately 33.487.
The second step is to multiply 33.487 by 5.
So 33.487 x 5 ≈ 167.435.
Problem 4
What will be the square root of (1121 + 4)?
The square root is approximately 33.6006.
Explanation
To find the square root, we need to find the sum of (1121 + 4). 1121 + 4 = 1125, and then √1125 ≈ 33.6006. Therefore, the square root of (1121 + 4) is approximately ±33.6006.
Problem 5
Find the perimeter of the rectangle if its length 'l' is √1121 units and the width 'w' is 38 units.
We find the perimeter of the rectangle as 142.974 units.
Explanation
Perimeter of the rectangle = 2 × (length + width).
Perimeter = 2 × (√1121 + 38) = 2 × (33.487 + 38) = 2 × 71.487 = 142.974 units.
FAQ on Square Root of 1121
1.What is √1121 in its simplest form?
2.Mention the factors of 1121.
3.Calculate the square of 1121.
4.Is 1121 a prime number?
5.1121 is divisible by?
6.How does learning Algebra help students in Philippines make better decisions in daily life?
7.How can cultural or local activities in Philippines support learning Algebra topics such as Square Root of 1121?
8.How do technology and digital tools in Philippines support learning Algebra and Square Root of 1121?
9.Does learning Algebra support future career opportunities for students in Philippines?
Important Glossaries for the Square Root of 1121
- Square root: A square root is the inverse of a square. Example: 4^2 = 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: Prime factorization involves breaking down a composite number into its prime factors.
- Long division method: A technique used to find the square root of non-perfect square numbers through a step-by-step division process.
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Jaskaran Singh Saluja
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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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