Square Root of 5329
2026-02-28 10:07 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 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.

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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.

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Problem 1

Can you help Max find the area of a square box if its side length is given as √5329?

Okay, lets begin

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.

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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?

Okay, lets begin

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.

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Problem 3

Calculate √5329 x 5.

Okay, lets begin

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.

Well explained 👍

Problem 4

What will be the square root of (5329 + 71)?

Okay, lets begin

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.

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Problem 5

Find the perimeter of the rectangle if its length ‘l’ is √5329 units and the width ‘w’ is 38 units.

Okay, lets begin

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.

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FAQ on Square Root of 5329

1.What is √5329 in its simplest form?

The prime factorization of 5329 is 73 x 73, so the simplest form of √5329 = √(73 x 73) = 73.

2.Is 5329 a perfect square?

Yes, 5329 is a perfect square, as it can be expressed as 73 x 73.

3.Calculate the square of 5329.

To find the square of 5329, we multiply the number by itself, that is 5329 x 5329 = 28,398,241.

4.Is 5329 a prime number?

5329 is not a prime number, as it has more than two factors.

5.What is the significance of perfect squares like 5329?

Perfect squares are significant in mathematical problems and real-world applications as they simplify calculations, especially in geometry and algebra, where square roots are needed.

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.

Fun Fact

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