126 LearnersLast updated on May 26th, 2025
Square of 81
The product of multiplying an integer by itself is the square of a number. Squares are used in programming, calculating areas, and so on. In this topic, we will discuss the square of 81.
What is the Square of 81
The square of a number is the product of the number by itself. The square of 81 is 81 × 81. The square of a number always ends in 0, 1, 4, 5, 6, or 9. We write it in math as 81², where 81 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 81 is 81 × 81 = 6561. Square of 81 in exponential form: 81² Square of 81 in arithmetic form: 81 × 81
How to Calculate the Value of Square of 81
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 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 81. Step 1: Identify the number. Here, the number is 81. Step 2: Multiplying the number by itself, we get, 81 × 81 = 6561. The square of 81 is 6561.
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 81 So: 81² = 81 × 81 = 6561
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 81. Step 1: Enter the number in the calculator Enter 81 in the calculator. Step 2: Multiply the number by itself using the multiplication button (×) That is 81 × 81 Step 3: Press the equal to button to find the answer Here, the square of 81 is 6561. Tips and Tricks for the Square of 81 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 81
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 while using the formula.
The formula to find the square of the number is a². Instead, students may use 81² with (8 + 1)² or (80 + 1)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 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 81
Problem 1
Find the length of the square, where the area of the square is 6561 cm².
The area of a square = a² So, the area of a square = 6561 cm² So, the length = √6561 = 81. The length of each side = 81 cm
Explanation
The length of a square is 81 cm. Because the area is 6561 cm², the length is √6561 = 81.
Problem 2
Emma is planning to tile her square patio of length 81 feet. The cost to tile a foot is 5 dollars. Then how much will it cost to tile the full patio?
The length of the patio = 81 feet The cost to tile 1 square foot of the patio = 5 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 = 81 Therefore, the area of the patio = 81² = 81 × 81 = 6561. The cost to tile the patio = 6561 × 5 = 32805. The total cost = 32805 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 32805 dollars.
Problem 3
Find the area of a circle whose radius is 81 meters.
The area of the circle = 20,612.16 m²
Explanation
The area of a circle = πr² Here, r = 81 Therefore, the area of the circle = π × 81² = 3.14 × 81 × 81 = 20,612.16 m².
Problem 4
The area of the square is 6561 cm². Find the perimeter of the square.
The perimeter of the square is 324 cm.
Explanation
The area of the square = a² Here, the area is 6561 cm² The length of the side is √6561 = 81 Perimeter of the square = 4a Here, a = 81 Therefore, the perimeter = 4 × 81 = 324 cm.
Problem 5
Find the square of 82.
The square of 82 is 6724.
Explanation
The square of 82 is multiplying 82 by 82. So, the square = 82 × 82 = 6724.
FAQs on Square of 81
1.What is the square of 81?
2.What is the square root of 81?
3.Is 81 a prime number?
4.What are the first few multiples of 81?
5.What is the square of 80?
6.How does learning Algebra help students in Australia make better decisions in daily life?
7.How can cultural or local activities in Australia support learning Algebra topics such as Square of 81?
8.How do technology and digital tools in Australia support learning Algebra and Square of 81?
9.Does learning Algebra support future career opportunities for students in Australia?
Important Glossaries for Square 81.
Integer: A whole number that can be positive, negative, or zero. Perfect Square: A number that is the square of an integer. For example, 81 is a perfect square because it is 9². Exponent: A mathematical notation indicating the number of times a number is multiplied by itself. For example, in 81², 2 is the exponent. Square Root: A value that, when multiplied by itself, gives the original number. For example, the square root of 81 is 9. Multiplication: The process of combining equal groups to find the total number of items.
Explore More algebra
![Important Math Links Icon]()
Previous to Square of 81
About BrightChamps in Australia
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.
