120 LearnersLast updated on May 26th, 2025
Square Root of 1161
If a number is multiplied by the same number, the result is a square. The inverse of squaring a number is finding its square root. The square root has applications in fields such as vehicle design, finance, etc. Here, we will discuss the square root of 1161.
What is the Square Root of 1161?
The square root is the inverse of squaring a number. 1161 is not a perfect square. The square root of 1161 is expressed in both radical and exponential form. In radical form, it is expressed as √1161, whereas in exponential form it is (1161)^(1/2). √1161 ≈ 34.076, which is an irrational number because it cannot be expressed in the form p/q, where p and q are integers and q ≠ 0.
Finding the Square Root of 1161
The prime factorization method is used for perfect square numbers. However, for non-perfect square numbers, methods like 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 1161 by Prime Factorization Method
The product of prime factors is the prime factorization of a number. Now let us look at how 1161 is broken down into its prime factors.
Step 1: Finding the prime factors of 1161 Breaking it down, we get 3 x 3 x 3 x 43: 3^3 x 43^1
Step 2: Now we have found the prime factors of 1161. The second step is to make pairs of those prime factors. Since 1161 is not a perfect square, the digits of the number can’t be grouped in pairs. Therefore, calculating √1161 using prime factorization alone is not possible.
Square Root of 1161 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 1161, we need to group it as 11 and 61.
Step 2: Now we need to find n whose square is 11 or less. We can say n is 3 because 3 x 3 = 9, which is less than 11. Now the quotient is 3, and after subtracting 9 from 11, the remainder is 2.
Step 3: Bring down 61 to make the new dividend 261. Add the last divisor with the quotient from the previous step, making it 6, which will be our new divisor.
Step 4: Now find n such that 6n x n is less than or equal to 261. We can try n = 4, which gives us 64 x 4 = 256.
Step 5: Subtract 256 from 261, leaving a remainder of 5. The quotient is now 34.
Step 6: Since the remainder is less than the divisor, we need to add a decimal point. Adding the decimal point allows us to bring down two zeroes, making the new dividend 500.
Step 7: Find the new divisor by adding 4 to the previous divisor, making it 68. Try n = 7, giving us 687 x 7 = 4809.
Step 8: Subtract 4809 from 50000 to get 191. Continue this process until you have the desired precision. So the square root of √1161 ≈ 34.076.
Square Root of 1161 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 1161 using the approximation method.
Step 1: Now we have to find the closest perfect squares around √1161. The smallest perfect square less than 1161 is 1089, and the largest perfect square greater than 1161 is 1225. √1161 falls somewhere between 33 and 35.
Step 2: Now we need to apply the formula: (Given number - smallest perfect square) / (Greater perfect square - smallest perfect square) Using the formula: (1161 - 1089) / (1225 - 1089) = 72 / 136 = 0.529 Using the formula, we approximate the decimal point of our square root. The next step is adding the integer part to the decimal number, which is 33 + 0.529 = 33.529, so the approximate square root of 1161 is 33.529.
Common Mistakes and How to Avoid Them in the Square Root of 1161
Students often make mistakes while finding the square root, such as forgetting about the negative square root or skipping steps in methods like long division. Now let us look at a few 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 has both positive and negative square roots. However, we usually consider only the positive square root, as it is the one most commonly used.
For example, √50 = 7.071, but there is also -7.071, 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.
For example, √(12 + 24) = √36, not √12 + √24.
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 to avoid mistakes when 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. This may happen in subtraction or elsewhere.
Square Root of 1161 Examples
Problem 1
Can you help Max find the area of a square box if its side length is given as √1161?
The area of the square is 1161 square units.
Explanation
The area of a square = side^2.
The side length is given as √1161.
Area of the square = side^2 = √1161 x √1161 = 1161.
Therefore, the area of the square box is 1161 square units.
Problem 2
A square-shaped building measuring 1161 square feet is built; if each of the sides is √1161, what will be the square feet of half of the building?
580.5 square feet
Explanation
We can just divide the given area by 2 as the building is square-shaped. Dividing 1161 by 2 gives us 580.5. So half of the building measures 580.5 square feet.
Problem 3
Calculate √1161 x 5.
170.38
Explanation
The first step is to find the square root of 1161, which is approximately 34.076.
The second step is to multiply 34.076 by 5.
So 34.076 x 5 = 170.38.
Problem 4
What will be the square root of (1150 + 11)?
The square root is approximately 34.076.
Explanation
To find the square root, we need to find the sum of (1150 + 11). 1150 + 11 = 1161, and then √1161 ≈ 34.076. Therefore, the square root of (1150 + 11) is approximately ±34.076.
Problem 5
Find the perimeter of the rectangle if its length ‘l’ is √1161 units and the width ‘w’ is 50 units.
The perimeter of the rectangle is approximately 168.152 units.
Explanation
Perimeter of the rectangle = 2 × (length + width).
Perimeter = 2 × (√1161 + 50) = 2 × (34.076 + 50) = 2 × 84.076 = 168.152 units.
FAQ on Square Root of 1161
1.What is √1161 in its simplest form?
2.Mention the factors of 1161.
3.Calculate the square of 1161.
4.Is 1161 a prime number?
5.1161 is divisible by?
6.How does learning Algebra help students in India make better decisions in daily life?
7.How can cultural or local activities in India support learning Algebra topics such as Square Root of 1161?
8.How do technology and digital tools in India support learning Algebra and Square Root of 1161?
9.Does learning Algebra support future career opportunities for students in India?
Important Glossaries for the Square Root of 1161
- Square root: A square root is the inverse of squaring a number. Example: 4^2 = 16, and the inverse of squaring is the square root, which is √16 = 4.
- Irrational number: An irrational number is a number that cannot be written as a simple fraction, i.e., in the form of p/q, where q is not zero and p and q are integers.
- Principal square root: A number has both positive and negative square roots. However, it is usually the positive square root that is used in real-world applications. This positive value is known as the principal square root.
- Approximation: A method used to find the approximate value of a number when an exact value is not needed or is difficult to obtain.
- Radical symbol: The symbol √ used to denote the square root of a number.
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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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