Square Root of 1159
2026-02-28 01:36 Diff
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Last updated on August 5, 2025

If a number is multiplied by itself, the result is a square. The inverse of the square is a square root. The square root is used in various fields such as vehicle design, finance, etc. Here, we will discuss the square root of 1159.

What is the Square Root of 1159?

The square root is the inverse of the square of the number. 1159 is not a perfect square. The square root of 1159 is expressed in both radical and exponential form. In the radical form, it is expressed as √1159, whereas (1159)^(1/2) in exponential form. √1159 ≈ 34.0454, 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 1159

The prime factorization method is used for perfect square numbers. However, for non-perfect square numbers, the prime factorization method is not applicable. Instead, long-division and approximation methods are used. Let us now learn the following methods:

  • Prime factorization method
     
  • Long division method
     
  • Approximation method

Square Root of 1159 by Prime Factorization Method

The product of prime factors is the prime factorization of a number. Now let us look at how 1159 is broken down into its prime factors.

Step 1: Finding the prime factors of 1159 Breaking it down, we get 7 × 13 × 127. Since 1159 is not a perfect square, these factors cannot be paired. Therefore, calculating 1159 using prime factorization as a perfect square is impossible.

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Square Root of 1159 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: Group the numbers from right to left. For 1159, group it as 59 and 11.

Step 2: Find n whose square is ≤ 11. We can say n as ‘3’ because 3 × 3 = 9, which is less than 11. Now the quotient is 3, and the remainder is 11 - 9 = 2.

Step 3: Bring down 59 to make the new dividend 259.

Step 4: Double the quotient and use it as the new divisor's first digit: 3 × 2 = 6.

Step 5: Now find a digit x such that 6x × x is less than or equal to 259. Try 4: 64 × 4 = 256.

Step 6: Subtract 256 from 259 to get the remainder 3.

Step 7: Since the remainder is less than the divisor, add a decimal point and two zeroes to continue. The new dividend is 300.

Step 8: Repeat the process to find more decimal places. So the square root of √1159 ≈ 34.0454.

Square Root of 1159 by Approximation Method

The approximation method is another approach for finding square roots. It is an easy method to estimate the square root of a given number. Now let us learn how to find the square root of 1159 using the approximation method.

Step 1: Find the closest perfect squares of √1159. The smallest perfect square less than 1159 is 1156 (34²) and the largest perfect square more than 1159 is 1225 (35²). √1159 falls between 34 and 35.

Step 2: Use interpolation to approximate: (1159 - 1156) / (1225 - 1156) = 3 / 69 ≈ 0.0435. Adding this to the lower bound: 34 + 0.0435 ≈ 34.0454. Therefore, the square root of 1159 is approximately 34.0454.

Common Mistakes and How to Avoid Them in the Square Root of 1159

Students often make errors while finding the square root, such as forgetting about the negative square root or skipping steps in the long division method. Here are a few common mistakes:

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Problem 1

Can you help Max find the area of a square box if its side length is given as √1159?

Okay, lets begin

The area of the square is approximately 1343.0881 square units.

Explanation

The area of the square = side².

The side length is given as √1159.

Area of the square = (√1159)² = 1159.

Well explained 👍

Problem 2

A square-shaped building measuring 1159 square feet is built. If each of the sides is √1159, what will be the square feet of half of the building?

Okay, lets begin

579.5 square feet

Explanation

We can divide the given area by 2 since the building is square-shaped. Dividing 1159 by 2 = 579.5. So half of the building measures 579.5 square feet.

Well explained 👍

Problem 3

Calculate √1159 × 5.

Okay, lets begin

170.227

Explanation

First, find the square root of 1159, which is approximately 34.0454. Then, multiply 34.0454 by 5. So, 34.0454 × 5 ≈ 170.227.

Well explained 👍

Problem 4

What will be the square root of (1150 + 9)?

Okay, lets begin

The square root is approximately 34.0454.

Explanation

To find the square root, calculate the sum of (1150 + 9) = 1159, and then find √1159 ≈ 34.0454.

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Problem 5

Find the perimeter of the rectangle if its length ‘l’ is √1159 units and the width ‘w’ is 38 units.

Okay, lets begin

The perimeter of the rectangle is approximately 144.0908 units.

Explanation

Perimeter of the rectangle = 2 × (length + width) Perimeter = 2 × (√1159 + 38) = 2 × (34.0454 + 38) ≈ 2 × 72.0454 ≈ 144.0908 units.

Well explained 👍

FAQ on Square Root of 1159

1.What is √1159 in its simplest form?

The prime factorization of 1159 is 7 × 13 × 127. Since these numbers cannot be paired, the simplest form of √1159 cannot be simplified further in radicals.

2.Mention the factors of 1159.

Factors of 1159 are 1, 7, 13, 91, 127, and 1159.

3.Calculate the square of 1159.

We get the square of 1159 by multiplying the number by itself: 1159 × 1159 = 1343281.

4.Is 1159 a prime number?

1159 is not a prime number, as it has more than two factors.

5.1159 is divisible by?

1159 is divisible by 1, 7, 13, 91, 127, and 1159.

Important Glossaries for the Square Root of 1159

  • Square root: A square root is the inverse operation of squaring a number. For example, 4² = 16, so the square root of 16 is √16 = 4.
  • Irrational number: An irrational number cannot be expressed as a simple fraction, where p and q are integers and q is not zero. Examples include √2 and √1159.
  • Principal square root: The principal square root is the non-negative square root of a number. For example, the principal square root of 16 is 4, not -4.
  • Prime factorization: Breaking down a number into its prime factors. For example, the prime factorization of 1159 is 7 × 13 × 127.
  • Approximation: Estimating a value to a certain degree of accuracy, such as finding √1159 ≈ 34.0454.

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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.

Fun Fact

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