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Last updated on May 26th, 2025

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Square Root of 1165

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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.

Square Root of 1165 for Omani Students
Professor Greenline from BrightChamps

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.

Professor Greenline from BrightChamps

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
Professor Greenline from BrightChamps

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.

Professor Greenline from BrightChamps

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.

Professor Greenline from BrightChamps

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.

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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

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Forgetting about the negative square root

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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.

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Square Root of 1165 Examples

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Max, the Girl Character from BrightChamps

Problem 1

Can you help Max find the area of a square box if its side length is given as √1165?

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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.

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Max, the Girl Character from BrightChamps

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?

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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.

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Max, the Girl Character from BrightChamps

Problem 3

Calculate √1165 x 5.

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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

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Max, the Girl Character from BrightChamps

Problem 4

What will be the square root of (1165 + 10)?

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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.

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Max, the Girl Character from BrightChamps

Problem 5

Find the perimeter of the rectangle if its length ‘l’ is √1165 units and the width ‘w’ is 38 units.

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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.

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FAQ on Square Root of 1165

1.What is √1165 in its simplest form?

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2.Mention the factors of 1165.

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3.Calculate the square of 1165.

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4.Is 1165 a prime number?

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5.1165 is divisible by?

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6.How does learning Algebra help students in Oman make better decisions in daily life?

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7.How can cultural or local activities in Oman support learning Algebra topics such as Square Root of 1165?

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8.How do technology and digital tools in Oman support learning Algebra and Square Root of 1165?

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9.Does learning Algebra support future career opportunities for students in Oman?

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Professor Greenline from BrightChamps

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.
Professor Greenline from BrightChamps

About BrightChamps in Oman

At BrightChamps, we understand algebra as more than symbols—it’s a key to unlocking many opportunities! Our mission is to help children across Oman gain important math skills, focusing today on the Square Root of 1165 with special attention to square roots—in an engaging, lively, and easy-to-follow manner. Whether your child is measuring how fast a roller coaster moves at Oman’s Dreamland Aqua Park, tracking local football scores, or managing their allowance for the latest gadgets, mastering algebra gives them confidence for everyday tasks. Our hands-on lessons make learning simple and fun. Because children in Oman learn differently, we adapt lessons to fit each learner’s style. From Muscat’s vibrant city life to beautiful natural landscapes, BrightChamps brings math to life, making it exciting throughout Oman. Let’s make square roots a joyful part of every child’s math journey!
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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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Max, the Girl Character from BrightChamps

Fun Fact

: He loves to play the quiz with kids through algebra to make kids love it.

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