Square Root of 1160
2026-02-28 08:35 Diff
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Last updated on August 5, 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 the field of vehicle design, finance, etc. Here, we will discuss the square root of 1160.

What is the Square Root of 1160?

The square root is the inverse of the square of the number. 1160 is not a perfect square. The square root of 1160 is expressed in both radical and exponential form. In the radical form it is expressed as, √1160, whereas (1160)^(1/2) in the exponential form. √1160 ≈ 34.057, 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 1160

The prime factorization method is used for perfect square numbers. However, the prime factorization method is not used for non-perfect square numbers where 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 1160 by Prime Factorization Method

The product of prime factors is the prime factorization of a number. Now let us look at how 1160 is broken down into its prime factors.

Step 1: Finding the prime factors of 1160 Breaking it down, we get 2 × 2 × 2 × 5 × 29 = 2^3 × 5^1 × 29^1

Step 2: Now we found out the prime factors of 1160. The second step is to make pairs of those prime factors. Since 1160 is not a perfect square, therefore the digits of the number can’t be grouped in pairs. Therefore, calculating 1160 using prime factorization is impossible.

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Square Root of 1160 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 1160, we need to group it as 60 and 11.

Step 2: Now we need to find n whose square is 11. We can say n as ‘3’ because 3 × 3 is lesser than or equal to 11. Now the quotient is 3; after subtracting 9 from 11, the remainder is 2.

Step 3: Now let us bring down 60, which is the new dividend. Add the old divisor with the same number 3 + 3; we get 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; we need to find the value of n.

Step 5: The next step is finding 6n × n ≤ 260. Let us consider n as 4, now 6 × 4 × 4 = 256.

Step 6: Subtract 256 from 260; the difference is 4, and the quotient is 34.

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 400.

Step 8: Now we need to find the new divisor that is 68 because 688 × 6 = 408.

Step 9: Subtracting 408 from 400, we get the result -8.

Step 10: Now the quotient is 34.0

Step 11: Continue doing these steps until we get two numbers after the decimal point. Suppose if there are no decimal values, continue till the remainder is zero. So the square root of √1160 is 34.05

Square Root of 1160 by Approximation Method

The approximation method is another method for finding the square roots; 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 1160 using the approximation method.

Step 1: Now we have to find the closest perfect square of √1160. The smallest perfect square less than 1160 is 1156 and the largest perfect square greater than 1160 is 1225. √1160 falls somewhere between 34 and 35

Step 2: Now we need to apply the formula that is (Given number - smallest perfect square) / (Greater perfect square - smallest perfect square) Going by the formula (1160 - 1156) ÷ (1225 - 1156) = 0.057 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, which is 34 + 0.057 = 34.057, so the square root of 1160 is 34.057

Common Mistakes and How to Avoid Them in the Square Root of 1160

Students do make mistakes while finding the square root, likewise forgetting about the negative square root. Skipping long division methods, etc. Now let us look at a few of those mistakes that students tend to make in detail.

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Problem 1

Can you help Max find the area of a square box if its side length is given as √1160?

Okay, lets begin

The area of the square is 1160 square units.

Explanation

The area of the square = side².

The side length is given as √1160.

Area of the square = side² = √1160 × √1160 = 1160

Therefore, the area of the square box is 1160 square units.

Well explained 👍

Problem 2

A square-shaped building measuring 1160 square feet is built. If each of the sides is √1160, what will be the square feet of half of the building?

Okay, lets begin

580 square feet

Explanation

We can just divide the given area by 2 as the building is square-shaped.

Dividing 1160 by 2 = we get 580

So half of the building measures 580 square feet.

Well explained 👍

Problem 3

Calculate √1160 × 5.

Okay, lets begin

170.285

Explanation

The first step is to find the square root of 1160, which is approximately 34.057. The second step is to multiply 34.057 with 5. So 34.057 × 5 = 170.285

Well explained 👍

Problem 4

What will be the square root of (1160 + 9)?

Okay, lets begin

The square root is 34

Explanation

To find the square root, we need to find the sum of (1160 + 9). 1160 + 9 = 1169, and then √1169 ≈ 34.184 Therefore, the square root of (1160 + 9) is approximately ±34.184

Well explained 👍

Problem 5

Find the perimeter of the rectangle if its length ‘l’ is √1160 units and the width ‘w’ is 50 units.

Okay, lets begin

We find the perimeter of the rectangle as 168.114 units.

Explanation

Perimeter of the rectangle = 2 × (length + width)

Perimeter = 2 × (√1160 + 50) = 2 × (34.057 + 50) = 2 × 84.057 = 168.114 units.

Well explained 👍

FAQ on Square Root of 1160

1.What is √1160 in its simplest form?

The prime factorization of 1160 is 2 × 2 × 2 × 5 × 29 so the simplest form of √1160 = √(2 × 2 × 2 × 5 × 29)

2.Mention the factors of 1160.

Factors of 1160 are 1, 2, 4, 5, 8, 10, 20, 29, 40, 58, 116, 145, 232, 290, 580, and 1160.

3.Calculate the square of 1160.

We get the square of 1160 by multiplying the number by itself, that is 1160 × 1160 = 1,345,600

4.Is 1160 a prime number?

1160 is not a prime number, as it has more than two factors.

5.1160 is divisible by?

1160 has many factors; those are 1, 2, 4, 5, 8, 10, 20, 29, 40, 58, 116, 145, 232, 290, 580, and 1160.

Important Glossaries for the Square Root of 1160

  • 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 the reason it is also known as a principal square root.
  • Prime factorization: Prime factorization is expressing a number as the product of its prime factors. For example, the prime factorization of 20 is 2 × 2 × 5.
  • Long division method: The long division method is a step-by-step process used to find the square roots of numbers, especially those that are not perfect squares.

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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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