126 LearnersLast updated on May 26th, 2025
Square Root of 1329
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.
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.
Mistake 1
Forgetting about the negative square root
It is important to remember that a number has both positive and negative square roots. However, in practical applications, we often consider only the positive root.
For example, √1329 ≈ ±36.454, but we typically use the positive value.
Mistake 2
Not adding the square root symbol properly
Misplacing the square root symbol can lead to errors. Simplifying numbers within the square root before proceeding can help avoid mistakes.
For example, √(25 + 9) = √34 is correct, but √25 + √9 = 5 + 3 = 8 is incorrect.
Mistake 3
Not finding the correct value of a non-perfect square
Students should learn to approximate non-perfect squares accurately.
For example, √1329 should not be approximated as 36; the correct approximation is 36.454.
Mistake 4
Confusing the square root symbol with the cube root
It's crucial to differentiate between square and cube roots.
For example, √1329 and ∛1329 are different operations.
Mistake 5
Making mistakes in long division
The long division method involves multiple steps. Skipping or miscalculating any step can lead to incorrect results. Careful attention to each step can prevent errors.
Square Root of 1329 Examples
Problem 1
Can you help Max find the area of a square box if its side length is given as √1329?
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.
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?
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.
Problem 3
Calculate √1329 × 5.
182.27
Explanation
First, find the square root of 1329, which is approximately 36.454.
Then multiply by 5. 36.454 × 5 = 182.27.
Problem 4
What will be the square root of (1300 + 29)?
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.
Problem 5
Find the perimeter of a rectangle if its length ‘l’ is √1329 units and the width ‘w’ is 40 units.
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.
FAQ on Square Root of 1329
1.What is √1329 in its simplest form?
2.Mention the factors of 1329.
3.Calculate the square of 1329.
4.Is 1329 a prime number?
5.What numbers is 1329 divisible by?
6.How does learning Algebra help students in India make better decisions in daily life?
7.How can cultural or local activities in India support learning Algebra topics such as Square Root of 1329?
8.How do technology and digital tools in India support learning Algebra and Square Root of 1329?
9.Does learning Algebra support future career opportunities for students in India?
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
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