Square Root of 529
2026-02-28 23:47 Diff
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Last updated on September 30, 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 the field of vehicle design, finance, etc. Here, we will discuss the square root of 529.

What is the Square Root of 529?

The square root is the inverse of the square of the number. 529 is a perfect square. The square root of 529 is expressed in both radical and exponential form. In the radical form, it is expressed as √529, whereas (529)(1/2) in the exponential form. √529 = 23, 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 529

The prime factorization method is used for perfect square numbers. Since 529 is a perfect square, we can use the prime factorization method. Other methods such as the long division method or approximation method can also be used but are not necessary in this case.

  1. Prime factorization method
  2. Long division method
  3. Approximation method

Square Root of 529 by Prime Factorization Method

The product of prime factors is the prime factorization of a number. Now let us look at how 529 is broken down into its prime factors.

Step 1: Finding the prime factors of 529 529 = 23 × 23 = 232

Step 2: Since 529 is a perfect square, we can take one number from each pair of identical factors.

The square root of 529 is 23.

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Square Root of 529 by Long Division Method

The long division method can also be used for perfect square numbers. It involves dividing the number into groups from right to left and finding the square root step by step.

Step 1: Group the digits of 529 from right to left as (5, 29).

Step 2: Find a number whose square is less than or equal to 5. The number is 2 because 2 × 2 = 4. Subtract 4 from 5, giving a remainder of 1. Bring down the next pair, 29, making it 129.

Step 3: Double the quotient (2) to get 4, which will be part of our new divisor.

Step 4: Find a digit (n) such that 4n × n ≤ 129. n is 3 because 43 × 3 = 129.

Step 5: Subtract 129 from 129 to get a remainder of 0. The quotient is 23, so the square root of 529 is 23.

Square Root of 529 by Approximation Method

Since 529 is a perfect square, the approximation method isn't necessary. However, for illustration:

Step 1: Identify two perfect squares between which 529 lies. Here, it is already a perfect square, i.e., 232 = 529.

Step 2: Since 529 is a perfect square, its square root is exactly 23.

Common Mistakes and How to Avoid Them in the Square Root of 529

Students sometimes make errors while finding the square root, such as forgetting about the negative square root or making calculation mistakes. Here are a few common mistakes and how to avoid them:

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Problem 1

What is the side length of a square with an area of 529 square units?

Okay, lets begin

The side length of the square is 23 units.

Explanation

The area of the square = side2.

Given that the area is 529, we solve for the side length: side = √529 = 23.

Therefore, the side length is 23 units.

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Problem 2

If a square-shaped tile has a side length of √529, what is the perimeter of the tile?

Okay, lets begin

The perimeter of the tile is 92 units.

Explanation

The side length of the tile is √529 = 23.

The perimeter of a square is 4 times the side length, so the perimeter is 4 × 23 = 92 units.

Well explained 👍

Problem 3

Calculate 2 × √529.

Okay, lets begin

46

Explanation

The square root of 529 is 23.

Therefore, 2 × √529 = 2 × 23 = 46.

Well explained 👍

Problem 4

What is the square root of (529 - 4)?

Okay, lets begin

The square root is 22.

Explanation

First, find the difference: 529 - 4 = 525.

The square root of 525 is approximately 22.91, but this question seems to have an error as 525 is not a perfect square.

The correct context would be using perfect squares.

Well explained 👍

Problem 5

What is the perimeter of a rectangle if its length ‘l’ is √529 units and the width ‘w’ is 10 units?

Okay, lets begin

The perimeter of the rectangle is 66 units.

Explanation

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

Perimeter = 2 × (√529 + 10) = 2 × (23 + 10) = 2 × 33 = 66 units.

Well explained 👍

FAQ on Square Root of 529

1.What is √529 in its simplest form?

The prime factorization of 529 is 23 × 23, so the simplest form of √529 is 23.

2.Is 529 a perfect square?

Yes, 529 is a perfect square because it can be expressed as 23 × 23.

3.What are the factors of 529?

The factors of 529 are 1, 23, and 529.

4.Calculate the square of 23.

The square of 23 is 529, since 23 × 23 = 529.

5.Is 529 a prime number?

No, 529 is not a prime number because it has more than two factors.

Important Glossaries for the Square Root of 529

  • Square root: A square root is the inverse of a square. Example: 232 = 529 and the inverse of the square is the square root, which is √529 = 23.
  • Perfect square: A number that can be expressed as the product of an integer with itself.
  • Rational number: A number that can be expressed in the form p/q, where p and q are integers and q ≠ 0.
  • Prime factorization: The process of expressing a number as the product of its prime factors.
  • Perimeter: The total distance around a two-dimensional shape, such as a square or rectangle.

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