Square Root of 1329
2026-02-28 23:14 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 squaring a number is finding its square root. Square roots are used in fields like vehicle design, finance, and more. Here, we will discuss the square root of 1329.

What is the Square Root of 1329?

The square root is the inverse operation of squaring a number. 1329 is not a perfect square. The square root of 1329 is expressed in both radical and exponential form. In radical form, it is expressed as √1329, whereas in exponential form it is expressed as (1329)^(1/2). √1329 ≈ 36.454, which is an irrational number because it cannot be expressed as a fraction of two integers.

Finding the Square Root of 1329

The prime factorization method is typically used for perfect square numbers. However, for non-perfect square numbers, methods like long-division and approximation are used. Let us now learn about these methods: 

  • Long division method
  • Approximation method

Square Root of 1329 by Long Division Method

The long division method is particularly useful for non-perfect square numbers. Below are the steps to find the square root using the long division method:

Step 1: Begin by grouping the digits of the number starting from the right. For 1329, the groups are 29 and 13.

Step 2: Determine the largest integer n such that n^2 is less than or equal to 13. Here, n is 3, since 3^2 = 9.

Step 3: Subtract 9 from 13, leaving a remainder of 4, and bring down the next group, 29, to make it 429.

Step 4: Double the current quotient (3), making it 6, and use it as the starting digits of the new divisor, 6_. Determine the largest digit x such that 6x * x ≤ 429. Here, x is 6.

Step 5: Subtract 396 (66 * 6) from 429, leaving a remainder of 33.

Step 6: Bring down pairs of zeros, continuing the long-division process to refine the decimal places.

Step 7: Continue this process until the desired precision is achieved. The square root of 1329 is approximately 36.45.

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Square Root of 1329 by Approximation Method

The approximation method is a simpler way to find the square root of a number. Here's how to find the square root of 1329 using approximation:

Step 1: Identify the closest perfect squares around 1329. The smaller perfect square is 1296 (36^2) and the larger is 1369 (37^2). Thus, √1329 is between 36 and 37.

Step 2: Use interpolation to estimate the square root. Using approximation, √1329 ≈ 36.454.

Common Mistakes and How to Avoid Them in the Square Root of 1329

Students often make mistakes while finding square roots, such as forgetting about negative roots or skipping steps in the long division method. Let's explore some common mistakes 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 √1329?

Okay, lets begin

The area of the square is approximately 1765.78 square units.

Explanation

The area of a square = side^2.

The side length is given as √1329.

Area = (√1329)^2 = 1329 square units.

Therefore, the area of the square box is approximately 1765.78 square units.

Well explained 👍

Problem 2

A square-shaped building measures 1329 square feet. If each of the sides is √1329, what will be the square feet of half of the building?

Okay, lets begin

664.5 square feet

Explanation

The area of the building is 1329 square feet.

Half of this area is calculated by dividing by 2. 1329 / 2 = 664.5 square feet.

So, half of the building measures 664.5 square feet.

Well explained 👍

Problem 3

Calculate √1329 × 5.

Okay, lets begin

182.27

Explanation

First, find the square root of 1329, which is approximately 36.454.

Then multiply by 5. 36.454 × 5 = 182.27.

Well explained 👍

Problem 4

What will be the square root of (1300 + 29)?

Okay, lets begin

The square root is approximately 36.454.

Explanation

To find the square root, calculate the sum (1300 + 29) = 1329.

Then find the square root of 1329, which is approximately 36.454.

Therefore, the square root of (1300 + 29) is approximately ±36.454.

Well explained 👍

Problem 5

Find the perimeter of a rectangle if its length ‘l’ is √1329 units and the width ‘w’ is 40 units.

Okay, lets begin

The perimeter of the rectangle is approximately 152.91 units.

Explanation

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

Perimeter = 2 × (√1329 + 40) = 2 × (36.454 + 40) = 2 × 76.454 = 152.91 units.

Well explained 👍

FAQ on Square Root of 1329

1.What is √1329 in its simplest form?

The simplest form of √1329 is just √1329, as the number is not a perfect square and cannot be simplified further.

2.Mention the factors of 1329.

Factors of 1329 include 1, 3, 443, and 1329.

3.Calculate the square of 1329.

The square of 1329 is calculated as 1329 × 1329 = 1,766,241.

4.Is 1329 a prime number?

5.What numbers is 1329 divisible by?

1329 is divisible by 1, 3, 443, and 1329.

Important Glossaries for the Square Root of 1329

  • Square root: The square root of a number is the value that, when multiplied by itself, gives the original number. Example: The square root of 25 is 5.
  • Irrational number: An irrational number cannot be expressed as a fraction of two integers. It has a non-repeating, non-terminating decimal expansion.
  • Long division method: A technique used to divide two numbers, often employed to find the square root of non-perfect squares.
  • Approximation method: A method to estimate the square root of a number by identifying nearby perfect squares and interpolating.
  • Perfect square: A number that is the square of an integer. For example, 144 is a perfect square because it is 12 squared.

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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.