Square of 829
2026-02-28 08:18 Diff
https://brightchamps.com/en-us/math/algebra/square-of-829

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Last updated on August 5, 2025

The product of multiplying an integer by itself is the square of a number. The square is used in programming, calculating areas, and so on. In this topic, we will discuss the square of 829.

What is the Square of 829

The square of a number is the product of the number itself.

The square of 829 is 829 × 829.

The square of a number always ends in 0, 1, 4, 5, 6, or 9.

We write it in math as 829², where 829 is the base and 2 is the exponent.

The square of a positive and a negative number is always positive.

For example, 5² = 25; -5² = 25.

The square of 829 is 829 × 829 = 687241.

Square of 829 in exponential form: 829²

Square of 829 in arithmetic form: 829 × 829

How to Calculate the Value of Square of 829

The square of a number is multiplying the number by itself. So let’s learn how to find the square of a number. These are the common methods used to find the square of a number.

  • By Multiplication Method
     
  • Using a Formula
     
  • Using a Calculator

By the Multiplication Method

In this method, we will multiply the number by itself to find the square. The product here is the square of the number. Let’s find the square of 829.

Step 1: Identify the number. Here, the number is 829.

Step 2: Multiplying the number by itself, we get, 829 × 829 = 687241.

The square of 829 is 687241.

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Using a Formula (a²)

In this method, the formula a² is used to find the square of the number, where a is the number.

Step 1: Understanding the equation Square of a number = a² a² = a × a

Step 2: Identifying the number and substituting the value in the equation.

Here, ‘a’ is 829.

So: 829² = 829 × 829 = 687241

By Using a Calculator

Using a calculator to find the square of a number is the easiest method. Let’s learn how to use a calculator to find the square of 829.

Step 1: Enter the number in the calculator Enter 829 in the calculator.

Step 2: Multiply the number by itself using the multiplication button (×) That is 829 × 829

Step 3: Press the equal to button to find the answer Here, the square of 829 is 687241.

Tips and Tricks for the Square of 829

Tips and tricks make it easy for students to understand and learn the square of a number. To master the square of a number, these tips and tricks will help students.

  • The square of an even number is always an even number. For example, 6² = 36
     
  • The square of an odd number is always an odd number. For example, 5² = 25
     
  • The last digit of the square of a number is always 0, 1, 4, 5, 6, or 9.
     
  • If the square root of a number is a fraction or a decimal, then the number is not a perfect square. For example, √1.44 = 1.2
     
  • The square root of a perfect square is always a whole number. For example, √144 = 12.

Common Mistakes to Avoid When Calculating the Square of 829

Mistakes are common among kids when doing math, especially when it is finding the square of a number. Let’s learn some common mistakes to master the squaring of a number.

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Problem 1

Find the length of the square, where the area of the square is 687241 cm².

Okay, lets begin

The area of a square = a² So, the area of a square = 687241 cm² So, the length = √687241 = 829. The length of each side = 829 cm

Explanation

The length of a square is 829 cm.

Because the area is 687241 cm², the length is √687241 = 829.

Well explained 👍

Problem 2

Alice wants to plant grass on her square garden that is 829 feet long on each side. The cost to plant grass per square foot is 5 dollars. How much will it cost to plant the whole garden?

Okay, lets begin

The length of the garden = 829 feet The cost to plant grass per square foot = 5 dollars. To find the total cost to plant grass, we find the area of the garden, Area of the garden = area of the square = a² Here a = 829 Therefore, the area of the garden = 829² = 829 × 829 = 687241. The cost to plant the garden = 687241 × 5 = 3436205. The total cost = 3436205 dollars

Explanation

To find the cost to plant the garden, we multiply the area of the garden by the cost to plant per square foot.

So, the total cost is 3436205 dollars.

Well explained 👍

Problem 3

Find the area of a circle whose radius is 829 meters.

Okay, lets begin

The area of the circle = 2,159,417.94 m²

Explanation

The area of a circle = πr²

Here, r = 829

Therefore, the area of the circle = π × 829² = 3.14 × 829 × 829 = 2159417.94 m².

Well explained 👍

Problem 4

The area of a square is 687241 cm². Find the perimeter of the square.

Okay, lets begin

The perimeter of the square is 3316 cm.

Explanation

The area of the square = a²

Here, the area is 687241 cm²

The length of the side is √687241 = 829

Perimeter of the square = 4a

Here, a = 829

Therefore, the perimeter = 4 × 829 = 3316.

Well explained 👍

Problem 5

Find the square of 830.

Okay, lets begin

The square of 830 is 688900.

Explanation

The square of 830 is multiplying 830 by 830.

So, the square = 830 × 830 = 688900.

Well explained 👍

FAQs on Square of 829

1.What is the square of 829?

The square of 829 is 687241, as 829 × 829 = 687241.

2.What is the square root of 829?

The square root of 829 is ±28.79.

3.Is 829 a prime number?

Yes, 829 is a prime number; it is only divisible by 1 and 829.

4.What are the first few multiples of 829?

The first few multiples of 829 are 829, 1658, 2487, 3316, 4145, 4974, and so on.

5.What is the square of 828?

The square of 828 is 685584.

Important Glossaries for Square 829.

  • Prime number: A number that is only divisible by 1 and itself. For example, 2, 3, 5, 7, 829, etc.
     
  • Exponential form: A way of writing numbers using a base and an exponent. For example, 829² where 829 is the base and 2 is the exponent.
     
  • Square root: The inverse operation of squaring a number. The square root of a number is a value that, when multiplied by itself, gives the original number.
     
  • Perfect square: A number that is the square of an integer. For example, 144 is a perfect square because 12 × 12 = 144.
     
  • Area: The amount of space inside the boundary of a flat (2-dimensional) object such as a triangle or circle.

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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.