120 LearnersLast updated on May 26th, 2025
Square of 1009
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 1009.
What is the Square of 1009
The square of a number is the product of the number itself. The square of 1009 is 1009 × 1009. We write it in math as 1009², where 1009 is the base and 2 is the exponent. The square of a positive and a negative number is always positive.
For example, 5² = 25; (-5)² = 25.
The square of 1009 is 1009 × 1009 = 1,018,081.
Square of 1009 in exponential form: 1009²
Square of 1009 in arithmetic form: 1009 × 1009
How to Calculate the Value of Square of 1009
The square of a number is 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
- 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 1009.
Step 1: Identify the number. Here, the number is 1009.
Step 2: Multiplying the number by itself, we get: 1009 × 1009 = 1,018,081.
The square of 1009 is 1,018,081.
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 1009.
So: 1009² = 1009 × 1009 = 1,018,081
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 1009.
Step 1: Enter the number in the calculator. Enter 1009 in the calculator.
Step 2: Multiply the number by itself using the multiplication button (×). That is 1009 × 1009.
Step 3: Press the equal to button to find the answer. Here, the square of 1009 is 1,018,081.
Tips and Tricks for the Square of 1009
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 1009
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 in using the formula:
The formula to find the square of the number is a². Instead, students may use 1009² with (100 + 9)² incorrectly. 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 1009
Problem 1
Find the length of the square, where the area of the square is 1,018,081 cm².
The area of a square = a²
So, the area of a square = 1,018,081 cm²
So, the length = √1,018,081 = 1009.
The length of each side = 1009 cm
Explanation
The length of a square is 1009 cm. Because the area is 1,018,081 cm², the length is √1,018,081 = 1009.
Problem 2
Anna wants to tile her square floor of length 1009 feet. The cost to tile a square foot is 5 dollars. How much will it cost to tile the full floor?
The length of the floor = 1009 feet
The cost to tile 1 square foot of floor = 5 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 = 1009
Therefore, the area of the floor = 1009² = 1009 × 1009 = 1,018,081.
The cost to tile the floor = 1,018,081 × 5 = 5,090,405.
The total cost = 5,090,405 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 5,090,405 dollars.
Problem 3
Find the area of a circle whose radius is 1009 meters.
The area of the circle = 3,197,118.54 m²
Explanation
The area of a circle = πr²
Here, r = 1009
Therefore, the area of the circle = π × 1009²
= 3.14 × 1009 × 1009
= 3,197,118.54 m².
Problem 4
The area of the square is 1,018,081 cm². Find the perimeter of the square.
The perimeter of the square is 4,036 cm.
Explanation
The area of the square = a²
Here, the area is 1,018,081 cm²
The length of the side is √1,018,081 = 1009
Perimeter of the square = 4a
Here, a = 1009
Therefore, the perimeter = 4 × 1009 = 4,036 cm.
Problem 5
Find the square of 1010.
The square of 1010 is 1,020,100.
Explanation
The square of 1010 is multiplying 1010 by 1010. So, the square = 1010 × 1010 = 1,020,100.
FAQs on Square of 1009
1.What is the square of 1009?
2.What is the square root of 1009?
3.Is 1009 a prime number?
4.What are the first few multiples of 1009?
5.What is the square of 1010?
6.How does learning Algebra help students in United Kingdom make better decisions in daily life?
7.How can cultural or local activities in United Kingdom support learning Algebra topics such as Square of 1009?
8.How do technology and digital tools in United Kingdom support learning Algebra and Square of 1009?
9.Does learning Algebra support future career opportunities for students in United Kingdom?
Important Glossaries for Square of 1009
- Prime number: A number that is only divisible by 1 and itself. For example, 2, 3, 5, 7, 11, etc.
- Exponential form: Writing a number in the form of a power, such as 9² where 9 is the base and 2 is the exponent.
- Square root: The inverse operation of the square. The square root of a number is a number whose square is the number itself.
- Perfect square: A number that is the square of an integer. For example, 1, 4, 9, 16, etc.
- Area: The measure of the surface of a shape, calculated for squares as side length squared (a²).
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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.
Fun Fact
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