136 LearnersLast updated on May 30th, 2025
Square of 829
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.
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.
Mistake 1
Calculation errors:
Calculation errors mostly happen when students skip the steps or else by swapping the digits. To avoid it, students should double-check the answer. They can double-check by finding the square root of the solution they found.
For example, the square of 25 is 625, and the square root of 625 is ±25.
Mistake 2
Errors will be using the formula.
The formula to find the square of the number is a². Instead, students may use 829² with (8 + 29)² or (800 + 29)². So, students should check and use the correct formula and double-check the answers to avoid all the confusion.
Mistake 3
Confusing with square and square root.
Not understanding the concept of square and square root can lead to confusion in students. To avoid it, students should understand the concept that square and square root are inverse operations. The square of 5 is 25, and the square root of 25 is ±5.
Mistake 4
Errors in parentheses.
Ignoring the parentheses when finding the square of a number can lead to errors. So, students should understand parentheses. And do the operations in the correct order to avoid errors.
Mistake 5
Not practicing regularly.
Regular practice is required to master the square of a number. So students should do regular practice to avoid errors.
Solved Examples on Square of 829
Problem 1
Find the length of the square, where the area of the square is 687241 cm².
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.
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?
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.
Problem 3
Find the area of a circle whose radius is 829 meters.
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.
Problem 4
The area of a square is 687241 cm². Find the perimeter of the square.
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.
Problem 5
Find the square of 830.
The square of 830 is 688900.
Explanation
The square of 830 is multiplying 830 by 830.
So, the square = 830 × 830 = 688900.
FAQs on Square of 829
1.What is the square of 829?
2.What is the square root of 829?
3.Is 829 a prime number?
4.What are the first few multiples of 829?
5.What is the square of 828?
6.How does learning Algebra help students in United States make better decisions in daily life?
7.How can cultural or local activities in United States support learning Algebra topics such as Square of 829?
8.How do technology and digital tools in United States support learning Algebra and Square of 829?
9.Does learning Algebra support future career opportunities for students in United States?
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
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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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