132 LearnersLast updated on May 29th, 2025
Square of 522
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 the topic, we will discuss the square of 522.
What is the Square of 522
The square of a number is the product of the number itself.
The square of 522 is 522 × 522.
The square of a number always ends in 0, 1, 4, 5, 6, or 9. We write it in math as 522², where 522 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 522 is 522 × 522 = 272,484.
Square of 522 in exponential form: 522²
Square of 522 in arithmetic form: 522 × 522
How to Calculate the Value of Square of 522
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 522.
Step 1: Identify the number. Here, the number is 522.
Step 2: Multiplying the number by itself, we get, 522 × 522 = 272,484.
The square of 522 is 272,484.
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 522
So: 522² = 522 × 522 = 272,484
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 522.
Step 1: Enter the number in the calculator. Enter 522 in the calculator.
Step 2: Multiply the number by itself using the multiplication button (×). That is 522 × 522.
Step 3: Press the equal to button to find the answer Here, the square of 522 is 272,484.
Tips and Tricks for the Square of 522
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 522
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 522² with (5 + 2 + 2)² or (500 + 20 + 2)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 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 522
Problem 1
Find the length of the square, where the area of the square is 272,484 cm².
The area of a square = a²
So, the area of a square = 272,484 cm²
So, the length = √272,484 = 522.
The length of each side = 522 cm
Explanation
The length of a square is 522 cm. Because the area is 272,484 cm² the length is √272,484 = 522.
Problem 2
Emma is planning to paint her square wall of length 522 feet. The cost to paint a foot is 2 dollars. Then how much will it cost to paint the full wall?
The length of the wall = 522 feet
The cost to paint 1 square foot of wall = 2 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 = 522
Therefore, the area of the wall = 522² = 522 × 522 = 272,484.
The cost to paint the wall = 272,484 × 2 = 544,968.
The total cost = 544,968 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 544,968 dollars.
Problem 3
Find the area of a circle whose radius is 522 meters.
The area of the circle = 856,330.64 m²
Explanation
The area of a circle = πr²
Here, r = 522
Therefore, the area of the circle = π × 522² = 3.14 × 522 × 522 = 856,330.64 m².
Problem 4
The area of the square is 272,484 cm². Find the perimeter of the square.
The perimeter of the square is 2,088 cm.
Explanation
The area of the square = a²
Here, the area is 272,484 cm²
The length of the side is √272,484 = 522
Perimeter of the square = 4a
Here, a = 522
Therefore, the perimeter = 4 × 522 = 2,088.
Problem 5
Find the square of 523.
The square of 523 is 273,529.
Explanation
The square of 523 is multiplying 523 by 523.
So, the square = 523 × 523 = 273,529.
FAQs on Square of 522
1.What is the square of 522?
2.What is the square root of 522?
3.Is 522 a prime number?
4.What are the first few multiples of 522?
5.What is the square of 521?
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 522?
8.How do technology and digital tools in United States support learning Algebra and Square of 522?
9.Does learning Algebra support future career opportunities for students in United States?
Important Glossaries for Square 522.
- Perfect square: A number that is the square of an integer. For example, 16 is a perfect square because it is 4².
- Exponent: A number that indicates how many times the base is multiplied by itself. For example, in 3², 2 is the exponent.
- Square: The result of multiplying a number by itself. For example, the square of 4 is 16.
- Square root: A value that, when multiplied by itself, gives the original number. For example, the square root of 49 is 7.
- Even number: A number that is divisible by 2. For example, 4, 6, 8, and 10 are even numbers.
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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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