130 LearnersLast updated on May 26th, 2025
Square Root of 5329
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 such as vehicle design, finance, etc. Here, we will discuss the square root of 5329.
What is the Square Root of 5329?
The square root is the inverse of the square of the number. 5329 is a perfect square. The square root of 5329 is expressed in both radical and exponential form. In the radical form, it is expressed as √5329, whereas (5329)^(1/2) in the exponential form. √5329 = 73, which is a rational number because it can be expressed in the form of p/q, where p and q are integers and q ≠ 0.
Finding the Square Root of 5329
The prime factorization method is used for perfect square numbers. For non-perfect square numbers, the long-division method and approximation method are used. Since 5329 is a perfect square, let us use the prime factorization method:
- Prime factorization method
- Long division method
- Approximation method
Square Root of 5329 by Prime Factorization Method
The product of prime factors is the Prime factorization of a number. Now let us look at how 5329 is broken down into its prime factors.
Step 1: Finding the prime factors of 5329. Breaking it down, we get 73 x 73: 73^2.
Step 2: Now, we found out the prime factors of 5329. Since it is a perfect square, the square root of 5329 can be calculated as the product of one factor from each pair, which is 73.
Square Root of 5329 by Long Division Method
The long division method is particularly used for non-perfect square numbers but can be applied to perfect squares as well. 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 5329, we need to group it as 53 and 29.
Step 2: Find a number whose square is less than or equal to 53. The number is 7, as 7 x 7 = 49.
Step 3: Subtract 49 from 53, which gives a remainder of 4. Bring down the next pair, 29, making the new dividend 429.
Step 4: Double the divisor (7), which gives 14, and find a digit n such that 14n x n is less than or equal to 429. The digit is 3, as 143 x 3 = 429.
Step 5: Subtract 429 from 429 to get 0. So, the square root of √5329 is 73.
Square Root of 5329 by Approximation Method
The approximation method is another way to find square roots, useful for non-perfect squares. Since 5329 is a perfect square, approximation is straightforward.
Step 1: Identify perfect squares closest to 5329. The number 5329 itself is a perfect square, falling exactly at 73 x 73. Thus, the square root of 5329 is precisely 73.
Common Mistakes and How to Avoid Them in the Square Root of 5329
Students do make mistakes while finding the square root, such as forgetting about the negative square root or skipping steps in the long division method. Now let us look at a few of those mistakes that students tend to make 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, we typically only consider the positive square root for practical applications.
For example: √5329 = 73, but there is also -73.
Mistake 2
Not adding the square root symbol in proper places
Not using the square root symbol properly is another mistake that children make. To resolve this, we need to teach children to simplify the numbers inside the square root before moving on.
For example: √(49+24) = √73 is correct, while √49 + √24 is incorrect.
Mistake 3
Not finding the correct value of a non-perfect square
The first step is to simplify the numbers inside the square root. This is vital to avoid mistakes when identifying the approximate value.
For example: √75 is not 7; the correct approximation is closer to 8.66.
Mistake 4
Confusing the square root symbol with the cube root
Students need to be taught the difference between cube root and square root constantly to avoid confusion.
For example: √64 and ∛64 are different; √64 = 8, while ∛64 = 4.
Mistake 5
Making mistakes in long division
Finding a square root using the Long Division method involves many steps, and students might skip a step accidentally, resulting in a wrong answer. This may occur during subtraction or elsewhere in the process.
Square root of 5329 Examples
Problem 1
Can you help Max find the area of a square box if its side length is given as √5329?
The area of the square is 5329 square units.
Explanation
The area of the square = side^2.
The side length is given as √5329.
Area of the square = side^2 = √5329 x √5329 = 73 × 73 = 5329.
Therefore, the area of the square box is 5329 square units.
Problem 2
A square-shaped building measuring 5329 square feet is built; if each of the sides is √5329, what will be the square feet of half of the building?
2664.5 square feet
Explanation
We can just divide the given area by 2 as the building is square-shaped.
Dividing 5329 by 2, we get 2664.5.
So, half of the building measures 2664.5 square feet.
Problem 3
Calculate √5329 x 5.
365
Explanation
The first step is to find the square root of 5329, which is 73.
The second step is to multiply 73 with 5.
So, 73 x 5 = 365.
Problem 4
What will be the square root of (5329 + 71)?
The square root is 74.
Explanation
To find the square root, we need to find the sum of (5329 + 71). 5329 + 71 = 5400, and then √5400 is approximately 73.48, but as 5400 is not a perfect square, it approximates to 73.48.
Problem 5
Find the perimeter of the rectangle if its length ‘l’ is √5329 units and the width ‘w’ is 38 units.
The perimeter of the rectangle is 222 units.
Explanation
Perimeter of the rectangle = 2 × (length + width).
Perimeter = 2 × (√5329 + 38) = 2 × (73 + 38) = 2 × 111 = 222 units.
FAQ on Square Root of 5329
1.What is √5329 in its simplest form?
2.Is 5329 a perfect square?
3.Calculate the square of 5329.
4.Is 5329 a prime number?
5.What is the significance of perfect squares like 5329?
6.How does learning Algebra help students in Indonesia make better decisions in daily life?
7.How can cultural or local activities in Indonesia support learning Algebra topics such as Square Root of 5329?
8.How do technology and digital tools in Indonesia support learning Algebra and Square Root of 5329?
9.Does learning Algebra support future career opportunities for students in Indonesia?
Important Glossaries for the Square Root of 5329
- Square root: A square root is the inverse of a square. Example: 8^2 = 64 and the inverse of the square is the square root, that is √64 = 8.
- Rational number: A rational number is a number that can be written in the form of p/q, where q is not equal to zero, and p and q are integers.
- Perfect square: A perfect square is a number that has an integer as its square root. For example, 5329 is a perfect square because √5329 = 73.
- Prime factorization: Prime factorization involves expressing a number as a product of its prime numbers. For example, 5329 = 73 x 73.
- Long division method: A technique used to find the square root of a number by dividing it into groups and using division steps to reach the answer sequentially.
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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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