127 LearnersLast updated on May 29th, 2025
Square of 524
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 524.
What is the Square of 524
The square of a number is the product of the number itself.
The square of 524 is 524 × 524.
The square of a number always ends in 0, 1, 4, 5, 6, or 9.
We write it in math as 524², where 524 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 524 is 524 × 524 = 274,576.
Square of 524 in exponential form: 524²
Square of 524 in arithmetic form: 524 × 524
How to Calculate the Value of Square of 524
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 524.
Step 1: Identify the number. Here, the number is 524.
Step 2: Multiplying the number by itself, we get, 524 × 524 = 274,576.
The square of 524 is 274,576.
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 524.
So: 524² = 524 × 524 = 274,576.
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 524.
Step 1: Enter the number in the calculator. Enter 524 in the calculator.
Step 2: Multiply the number by itself using the multiplication button (×). That is 524 × 524.
Step 3: Press the equal to button to find the answer. Here, the square of 524 is 274,576.
Tips and Tricks for the Square of 524
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 524
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 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 524² with (5 + 24)² or (500 + 24)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 524
Problem 1
Find the length of the square, where the area of the square is 274,576 cm².
The area of a square = a²
So, the area of a square = 274,576 cm²
So, the length = √274,576 = 524.
The length of each side = 524 cm
Explanation
The length of a square is 524 cm.
Because the area is 274,576 cm², the length is √274,576 = 524.
Problem 2
Tom is planning to paint his square wall of length 524 feet. The cost to paint a foot is 3 dollars. Then how much will it cost to paint the full wall?
The length of the wall = 524 feet.
The cost to paint 1 square foot of wall = 3 dollars.
To find the total cost to paint, we find the area of the wall.
Area of the wall = area of the square = a²
Here a = 524
Therefore, the area of the wall = 524² = 524 × 524 = 274,576.
The cost to paint the wall = 274,576 × 3 = 823,728.
The total cost = 823,728 dollars
Explanation
To find the cost to paint the wall, we multiply the area of the wall by the cost to paint per foot. So, the total cost is 823,728 dollars.
Problem 3
Find the area of a circle whose radius is 524 meters.
The area of the circle = 862,287.36 m²
Explanation
The area of a circle = πr²
Here, r = 524
Therefore, the area of the circle = π × 524² = 3.14 × 524 × 524 = 862,287.36 m².
Problem 4
The area of the square is 275,625 cm². Find the perimeter of the square.
The perimeter of the square is 2,100 cm
Explanation
The area of the square = a²
Here, the area is 275,625 cm²
The length of the side is √275,625 = 525
Perimeter of the square = 4a
Here, a = 525
Therefore, the perimeter = 4 × 525 = 2,100.
Problem 5
Find the square of 525.
The square of 525 is 275,625
Explanation
The square of 525 is multiplying 525 by 525.
So, the square = 525 × 525 = 275,625
FAQs on Square of 524
1.What is the square of 524?
2.What is the square root of 524?
3.Is 524 a prime number?
4.What are the first few multiples of 524?
5.What is the square of 523?
6.How does learning Algebra help students in Singapore make better decisions in daily life?
7.How can cultural or local activities in Singapore support learning Algebra topics such as Square of 524?
8.How do technology and digital tools in Singapore support learning Algebra and Square of 524?
9.Does learning Algebra support future career opportunities for students in Singapore?
Important Glossaries for Square of 524.
- Perfect Square: A number that is the square of an integer, like 274,576.
- Exponent: The power to which a number is raised, as in 524² where 2 is the exponent.
- Square Root: The number that, when multiplied by itself, gives the original number, such as √274,576 = 524.
- Multiplication: The mathematical operation of scaling one number by another, used in finding squares.
- Even Number: An integer divisible by 2, such as 524, which affects the parity of its square.
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About BrightChamps in Singapore
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.
