Last updated on May 26th, 2025
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.
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.
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:
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.
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.
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.
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.
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.
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.
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
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.
Calculate √1165 x 5.
170.64
First, find the square root of 1165, which is approximately 34.13. Then multiply 34.13 by 5. 34.13 x 5 = 170.65
What will be the square root of (1165 + 10)?
The square root is approximately 34.29.
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.
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.
Perimeter of the rectangle = 2 × (length + width)
Perimeter = 2 × (√1165 + 38) = 2 × (34.13 + 38) = 2 × 72.13 = 144.26 units.
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.
: He loves to play the quiz with kids through algebra to make kids love it.