114 LearnersLast updated on June 2nd, 2025
Square of 497
The product of multiplying an integer by itself is the square of a number. Square is used in programming, calculating areas, and so on. In this topic, we will discuss the square of 497.
What is the Square of 497
The square of a number is the product of the number itself.
The square of 497 is 497 × 497.
The square of a number always ends in 0, 1, 4, 5, 6, or 9.
We write it in math as 497², where 497 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 497 is 497 × 497 = 247,009.
Square of 497 in exponential form: 497²
Square of 497 in arithmetic form: 497 × 497
How to Calculate the Value of Square of 497
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 (a2)
- 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 497.
Step 1: Identify the number. Here, the number is 497.
Step 2: Multiplying the number by itself, we get, 497 × 497 = 247,009.
The square of 497 is 247,009.
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 497.
So: 497² = 497 × 497 = 247,009
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 497.
Step 1: Enter the number in the calculator. Enter 497 in the calculator.
Step 2: Multiply the number by itself using the multiplication button (×). That is 497 × 497.
Step 3: Press the equal to button to find the answer Here, the square of 497 is 247,009.
Tips and Tricks for the Square of 497
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 497
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 while using the formula.
The formula to find the square of the number is a². Instead, students may use 497² with (4 +9+7)² or (400 + 90 + 7)². So, students should check and use the correct formula and double-check the answers to avoid all the confusion.
Mistake 3
Confusing 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 497
Problem 1
Find the length of the square, where the area of the square is 247,009 cm².
The area of a square = a²
So, the area of a square = 247,009 cm²
So, the length = √247,009 = 497.
The length of each side = 497 cm
Explanation
The length of a square is 497 cm.
Because the area is 247,009 cm², the length is √247,009 = 497.
Problem 2
Sarah is planning to tile her square floor of length 497 feet. The cost to tile a foot is 4 dollars. Then how much will it cost to tile the full floor?
The length of the floor = 497 feet
The cost to tile 1 square foot of floor = 4 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 = 497
Therefore, the area of the floor = 497² = 497 × 497 = 247,009.
The cost to tile the floor = 247,009 × 4 = 988,036.
The total cost = 988,036 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 988,036 dollars.
Problem 3
Find the area of a circle whose radius is 497 meters.
The area of the circle = 775,699.59 m²
Explanation
The area of a circle = πr²
Here, r = 497
Therefore, the area of the circle = π × 497² = 3.14 × 497 × 497 = 775,699.59 m².
Problem 4
The area of the square is 247,009 cm². Find the perimeter of the square.
The perimeter of the square is
Explanation
The area of the square = a²
Here, the area is 247,009 cm²
The length of the side is √247,009 = 497
Perimeter of the square = 4a
Here, a = 497
Therefore, the perimeter = 4 × 497 = 1,988.
Problem 5
Find the square of 498.
The square of 498 is 248,004
Explanation
The square of 498 is multiplying 498 by 498.
So, the square = 498 × 498 = 248,004
FAQs on Square of 497
1.What is the square of 497?
2.What is the square root of 497?
3.Is 497 a prime number?
4.What are the first few multiples of 497?
5.What is the square of 496?
6.How does learning Algebra help students in Oman make better decisions in daily life?
7.How can cultural or local activities in Oman support learning Algebra topics such as Square of 497?
8.How do technology and digital tools in Oman support learning Algebra and Square of 497?
9.Does learning Algebra support future career opportunities for students in Oman?
Important Glossaries for Square 497.
- Perfect square: A perfect square is a number that is the square of an integer. For example, 49 is a perfect square of 7.
- Exponent: An exponent refers to the number of times a number is multiplied by itself. For example, in 10², 2 is the exponent.
- Area: The area is the amount of space taken up by a 2D shape, measured in square units.
- Calculator: A calculator is an electronic device used to perform mathematical calculations.
- Square root: The square root of a number is a value that, when multiplied by itself, gives the number. For example, the square root of 49 is ±7.
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About BrightChamps in Oman
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.
