133 LearnersLast updated on May 30th, 2025
Square of 823
The product of multiplying an integer by itself is the square of a number. Squares are used in programming, calculating areas, and so on. In this topic, we will discuss the square of 823.
What is the Square of 823
The square of a number is the product of the number itself.
The square of 823 is 823 × 823.
The square of a number always ends in 0, 1, 4, 5, 6, or 9.
We write it in math as 823², where 823 is the base and 2 is the exponent.
The square of a positive and a negative number is always positive.
For example, 5² = 25; (-5)² = 25.
The square of 823 is 823 × 823 = 677,329.
Square of 823 in exponential form: 823²
Square of 823 in arithmetic form: 823 × 823
How to Calculate the Value of Square of 823
The square of a number is found by multiplying the number by itself. Let's learn how to find the square of a number using common methods.
- By Multiplication Method
- Using a Formula
- Using a Calculator
By the Multiplication Method
In this method, we multiply the number by itself to find the square. The product here is the square of the number. Let’s find the square of 823.
Step 1: Identify the number. Here, the number is 823.
Step 2: Multiply the number by itself, we get, 823 × 823 = 677,329.
The square of 823 is 677,329.
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 823
So: 823² = 823 × 823 = 677,329
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 823.
Step 1: Enter the number in the calculator Enter 823 in the calculator.
Step 2: Multiply the number by itself using the multiplication button (×) That is 823 × 823
Step 3: Press the equal to button to find the answer
Here, the square of 823 is 677,329.
Tips and Tricks for the Square of 823
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 823
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 when using the formula.
The formula to find the square of the number is a². Instead, students may use 823² with (8 + 23)² or (800 + 23)². So students should check and use the correct formula and double-check the answers to avoid all 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 error.
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 823
Problem 1
Find the length of the square, where the area of the square is 677,329 cm².
The area of a square = a² So, the area of a square = 677,329 cm² So, the length = √677,329 = 823. The length of each side = 823 cm
Explanation
The length of a square is 823 cm.
Because the area is 677,329 cm², the length is √677,329 = 823.
Problem 2
Sarah is planning to tile her square floor of length 823 feet. The cost to tile a foot is 5 dollars. Then how much will it cost to tile the full floor?
The length of the floor = 823 feet The cost to tile 1 square foot of floor = 5 dollars. To find the total cost to tile, we find the area of the floor, Area of the floor = area of the square = a² Here a = 823 Therefore, the area of the floor = 823² = 823 × 823 = 677,329. The cost to tile the floor = 677,329 × 5 = 3,386,645. The total cost = 3,386,645 dollars
Explanation
To find the cost to tile the floor, we multiply the area of the floor by the cost to tile per foot.
So, the total cost is 3,386,645 dollars.
Problem 3
Find the area of a circle whose radius is 823 meters.
The area of the circle = 2,128,397.06 m²
Explanation
The area of a circle = πr²
Here, r = 823
Therefore, the area of the circle = π × 823² = 3.14 × 823 × 823 = 2,128,397.06 m².
Problem 4
The area of the square is 677,329 cm². Find the perimeter of the square.
The perimeter of the square is
Explanation
The area of the square = a²
Here, the area is 677,329 cm²
The length of the side is √677,329 = 823
Perimeter of the square = 4a
Here, a = 823
Therefore, the perimeter = 4 × 823 = 3,292.
Problem 5
Find the square of 824.
The square of 824 is 678,976
Explanation
The square of 824 is multiplying 824 by 824.
So, the square = 824 × 824 = 678,976
FAQs on Square of 823
1.What is the square of 823?
2.What is the square root of 823?
3.Is 823 a prime number?
4.What are the first few multiples of 823?
5.What is the square of 822?
6.How does learning Algebra help students in India make better decisions in daily life?
7.How can cultural or local activities in India support learning Algebra topics such as Square of 823?
8.How do technology and digital tools in India support learning Algebra and Square of 823?
9.Does learning Algebra support future career opportunities for students in India?
Important Glossaries for Square 823.
- Prime number: A number that is only divisible by 1 and itself. For example, 2, 3, 5, 7, 11, ...
- Exponential form: A way of writing numbers using a base and an exponent. For example, 9² where 9 is the base and 2 is the exponent.
- Square: The result of multiplying a number by itself. For example, the square of 4 is 16.
- Square root: The inverse operation of squaring, finding a number whose square is the given number. For example, the square root of 16 is 4.
- Perfect square: A number that is the square of an integer. For example, 36 is a perfect square because it is 6².
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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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