134 LearnersLast updated on May 29th, 2025
Square of 523
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 523.
What is the Square of 523
The square of a number is the product of the number by itself.
The square of 523 is 523 × 523.
The square of a number always ends in 0, 1, 4, 5, 6, or 9.
We write it in math as 523², where 523 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 523 is 523 × 523 = 273529.
Square of 523 in exponential form: 523²
Square of 523 in arithmetic form: 523 × 523
How to Calculate the Value of Square of 523
The square of a number is found by multiplying the number by itself. 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 523.
Step 1: Identify the number. Here, the number is 523.
Step 2: Multiplying the number by itself, we get, 523 × 523 = 273529.
The square of 523 is 273529.
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 523.
So: 523² = 523 × 523 = 273529
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 523.
Step 1: Enter the number in the calculator. Enter 523 in the calculator.
Step 2: Multiply the number by itself using the multiplication button (×). That is 523 × 523.
Step 3: Press the equal button to find the answer. Here, the square of 523 is 273529.
Tips and Tricks for the Square of 523
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 523
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 swap 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 using the formula.
The formula to find the square of the number is a². Instead, students may use 523² with (5+2+3)² or (500+20+3)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 523
Problem 1
Find the length of the square, where the area of the square is 273529 cm².
The area of a square = a²
So, the area of a square = 273529 cm²
So, the length = √273529 = 523.
The length of each side = 523 cm.
Explanation
The length of a square is 523 cm. Because the area is 273529 cm², the length is √273529 = 523.
Problem 2
Sarah is planning to tile her square patio with a length of 523 feet. The cost to tile a square foot is 10 dollars. Then how much will it cost to tile the full patio?
The length of the patio = 523 feet
The cost to tile 1 square foot of the patio = 10 dollars.
To find the total cost to tile, we find the area of the patio.
Area of the patio = area of the square = a²
Here a = 523
Therefore, the area of the patio = 523² = 523 × 523 = 273529.
The cost to tile the patio = 273529 × 10 = 2735290.
The total cost = 2735290 dollars.
Explanation
To find the cost to tile the patio, we multiply the area of the patio by the cost to tile per foot. So, the total cost is 2735290 dollars.
Problem 3
Find the area of a circle whose radius is 523 meters.
The area of the circle = 859,158.54 m²
Explanation
The area of a circle = πr²
Here, r = 523
Therefore, the area of the circle = π × 523² = 3.14 × 523 × 523 = 859158.54 m².
Problem 4
The area of the square is 273529 cm². Find the perimeter of the square.
The perimeter of the square is 2092 cm.
Explanation
The area of the square = a²
Here, the area is 273529 cm²
The length of the side is √273529 = 523
Perimeter of the square = 4a
Here, a = 523
Therefore, the perimeter = 4 × 523 = 2092 cm.
Problem 5
Find the square of 524.
The square of 524 is 274576
Explanation
The square of 524 is multiplying 524 by 524.
So, the square = 524 × 524 = 274576
FAQs on Square of 523
1.What is the square of 523?
2.What is the square root of 523?
3.Is 523 a prime number?
4.What are the first few multiples of 523?
5.What is the square of 525?
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 523?
8.How do technology and digital tools in United States support learning Algebra and Square of 523?
9.Does learning Algebra support future career opportunities for students in United States?
Important Glossaries for Square 523.
- Prime number: A number that is only divisible by 1 and itself. For example, 2, 3, 5, 7, 11, 13, etc.
- Exponential form: Writing a number in the form of a power. For example, 9², where 9 is the base and 2 is the exponent.
- Square root: The number whose square is the original number. For example, the square root of 16 is 4 because 4² = 16.
- Perfect square: A number that is the square of an integer. For example, 144 is a perfect square because it is 12².
- Area: The amount of space inside the boundary of a flat (2-dimensional) object such as a triangle or circle. In this context, it’s calculated in square units.
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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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