137 LearnersLast updated on May 30th, 2025
Square of 505
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 505.
What is the Square of 505
The square of a number is the product of the number itself.
The square of 505 is 505 × 505.
The square of a number always ends in 0, 1, 4, 5, 6, or 9.
We write it in math as 505², where 505 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 505 is 505 × 505 = 255025.
Square of 505 in exponential form: 505²
Square of 505 in arithmetic form: 505 × 505
How to Calculate the Value of Square of 505
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 505.
Step 1: Identify the number. Here, the number is 505.
Step 2: Multiplying the number by itself, we get, 505 × 505 = 255025.
The square of 505 is 255025.
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 505
So: 505² = 505 × 505 = 255025
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 505.
Step 1: Enter the number in the calculator Enter 505 in the calculator.
Step 2: Multiply the number by itself using the multiplication button (×). That is 505 × 505
Step 3: Press the equal to button to find the answer. Here, the square of 505 is 255025.
Tips and Tricks for the Square of 505
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 505
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 505² with (5 + 0 + 5)² or (500 + 5)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 505
Problem 1
Find the length of the square, where the area of the square is 255025 cm².
The area of a square = a²
So, the area of a square = 255025 cm²
So, the length = √255025 = 505.
The length of each side = 505 cm
Explanation
The length of a square is 505 cm.
Because the area is 255025 cm² the length is √255025 = 505.
Problem 2
Alice is planning to tile her square patio of length 505 feet. The cost to tile a foot is 10 dollars. Then how much will it cost to tile the full patio?
The length of the patio = 505 feet
The cost to tile 1 square foot of patio = is 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 = 505
Therefore, the area of the patio = 505² = 505 × 505 = 255025.
The cost to tile the patio = 255025 × 10 = 2550250.
The total cost = 2550250 dollars
Explanation
To find the cost to tile the patio, we multiply the area of the patio by cost to tile per foot.
So, the total cost is 2550250 dollars.
Problem 3
Find the area of a circle whose radius is 505 meters.
The area of the circle = 800625.26 m²
Explanation
The area of a circle = πr²
Here, r = 505
Therefore, the area of the circle = π × 505² = 3.14 × 505 × 505 = 800625.26 m².
Problem 4
The area of a square is 255025 cm². Find the perimeter of the square.
The perimeter of the square is 2020 cm
Explanation
The area of the square = a²
Here, the area is 255025 cm²
The length of the side is √255025 = 505
Perimeter of the square = 4a
Here, a = 505
Therefore, the perimeter = 4 × 505 = 2020 cm.
Problem 5
Find the square of 506.
The square of 506 is 256036
Explanation
The square of 506 is multiplying 506 by 506.
So, the square = 506 × 506 = 256036
FAQs on Square of 505
1.What is the square of 505?
2.What is the square root of 505?
3.Is 505 a prime number?
4.What are the first few multiples of 505?
5.What is the square of 500?
6.How does learning Algebra help students in Indonesia make better decisions in daily life?
7.How can cultural or local activities in Indonesia support learning Algebra topics such as Square of 505?
8.How do technology and digital tools in Indonesia support learning Algebra and Square of 505?
9.Does learning Algebra support future career opportunities for students in Indonesia?
Important Glossaries for Square of 505.
- Prime number: A number greater than 1 that is only divisible by 1 and itself.
- Exponential form: Writing a number in the form of a power, such as 505² where 505 is the base and 2 is the power.
- Square root: The square root of a number is a value that, when multiplied by itself, gives the original number.
- Perfect square: A number that is the square of an integer. For example, 25 is a perfect square because it is 5².
- Perimeter: The total distance around a 2D shape, like the perimeter of a square is calculated as 4 times the length of one side.
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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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