129 LearnersLast updated on May 26th, 2025
Square Root of 1165
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 1165.
What is the Square Root of 1165?
The square root is the inverse of the square of the number. 1165 is not a perfect square. The square root of 1165 is expressed in both radical and exponential form. In the radical form, it is expressed as √1165, whereas (1165)^(1/2) is in the exponential form. √1165 ≈ 34.128, 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 1165
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 1165 by Prime Factorization Method
The product of prime factors is the prime factorization of a number. Now let us look at how 1165 is broken down into its prime factors.
Step 1: Finding the prime factors of 1165 Breaking it down, we get 5 x 233.
Step 2: Since 1165 is not a perfect square, the digits of the number can’t be grouped in pairs. Therefore, calculating 1165 using prime factorization is not feasible for finding an exact square root.
Square Root of 1165 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 pair the digits of the number from right to left. In the case of 1165, we start with 16 and 11.
Step 2: Find the largest number whose square is less than or equal to 11. Here, it is 3 because 3 x 3 = 9. Subtract 9 from 11 to get the remainder 2.
Step 3: Bring down 65 to get the new dividend 265.
Step 4: Double the quotient obtained in Step 2 (which is 3) to get 6, and use it as the first part of our new divisor.
Step 5: Find a digit n such that 6n x n is less than or equal to 265. The best choice here is 4, giving us 64 x 4 = 256.
Step 6: Subtract 256 from 265 to get 9.
Step 7: Add decimal points and zeroes to the dividend as needed, and continue the process to get the square root accurate to two decimal places.
The square root of 1165 is approximately 34.13.
Square Root of 1165 by Approximation Method
The approximation method is a simpler way to find the square root of a given number. Now let us learn how to find the square root of 1165 using the approximation method.
Step 1: Identify the perfect squares closest to 1165. The closest perfect squares are 1156 (34^2) and 1225 (35^2).
Step 2: Since 1165 is closer to 1156, we know √1165 is slightly more than 34.
Step 3: Use linear approximation to find the decimal: (1165 - 1156) / (1225 - 1156) = 9 / 69 ≈ 0.13. Adding this to 34, we get approximately 34.13 as the square root of 1165.
Common Mistakes and How to Avoid Them in the Square Root of 1165
Students make mistakes while finding the square root, such as forgetting about the negative square root or skipping steps in methods like long division. Here are a few common mistakes in detail.
Mistake 1
Forgetting about the negative square root
It is important to remember that a number has both positive and negative square roots. However, we typically only consider the positive square root, as it is usually the required one.
For example, √1165 ≈ 34.13, but there is also -34.13, which should not be forgotten.
Mistake 2
Not adding square root symbol in proper places
Incorrectly using the square root symbol is another mistake. Simplify the numbers inside the square root first, then proceed.
For example, √(16 + 25) ≠ √16 + √25. The correct method is √(16 + 25) = √41.
Mistake 3
Not finding the correct value of a non-perfect square
Always simplify the numbers inside the square root first to avoid errors in identifying the approximate value.
For example, √50 ≠ 7; the correct answer is √50 ≈ 7.071.
Mistake 4
Confusing the square root symbol with the cube root
Students need to understand the difference between cube root and square root.
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, and students may accidentally skip a step, leading to incorrect answers. This could happen during subtraction or other steps.
Square Root of 1165 Examples
Problem 1
Can you help Max find the area of a square box if its side length is given as √1165?
The area of the square is approximately 1165 square units.
Explanation
The area of a square = side^2.
The side length is given as √1165. Area = (√1165)² = 1165.
Therefore, the area of the square box is approximately 1165 square units.
Problem 2
A square-shaped building measuring 1165 square feet is built; if each of the sides is √1165, what will be the square feet of half of the building?
582.5 square feet
Explanation
To find half the area of the building, divide the given area by 2. 1165 / 2 = 582.5
So half of the building measures 582.5 square feet.
Problem 3
Calculate √1165 x 5.
170.64
Explanation
First, find the square root of 1165, which is approximately 34.13. Then multiply 34.13 by 5. 34.13 x 5 = 170.65
Problem 4
What will be the square root of (1165 + 10)?
The square root is approximately 34.29.
Explanation
First, find the sum of (1165 + 10) = 1175. Then find the square root of 1175, which is approximately 34.29.
Therefore, the square root of (1165 + 10) is approximately ±34.29.
Problem 5
Find the perimeter of the rectangle if its length ‘l’ is √1165 units and the width ‘w’ is 38 units.
The perimeter of the rectangle is approximately 144.26 units.
Explanation
Perimeter of the rectangle = 2 × (length + width)
Perimeter = 2 × (√1165 + 38) = 2 × (34.13 + 38) = 2 × 72.13 = 144.26 units.
FAQ on Square Root of 1165
1.What is √1165 in its simplest form?
2.Mention the factors of 1165.
3.Calculate the square of 1165.
4.Is 1165 a prime number?
5.1165 is divisible by?
6.How does learning Algebra help students in United Kingdom make better decisions in daily life?
7.How can cultural or local activities in United Kingdom support learning Algebra topics such as Square Root of 1165?
8.How do technology and digital tools in United Kingdom support learning Algebra and Square Root of 1165?
9.Does learning Algebra support future career opportunities for students in United Kingdom?
Important Glossaries for the Square Root of 1165
- Square root: A square root is the inverse of a square. Example: 6^2 = 36, and the inverse of the square is the square root, which is √36 = 6.
- Irrational number: An irrational number is a number that cannot be written as a fraction p/q, where q is not equal to zero and p and q are integers.
- Divisor: A number by which another number is to be divided. In the division 1165 ÷ 5, 5 is the divisor.
- Perfect square: A number that is the square of an integer. For example, 144 is a perfect square because it is 12^2.
- Approximation: A value or number that is close to the exact value but not exact. For example, √1165 ≈ 34.13 is an approximation.
Explore More algebra
About BrightChamps in United Kingdom
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.
Fun Fact
: He loves to play the quiz with kids through algebra to make kids love it.
