111 LearnersLast updated on May 26th, 2025
Square of -81
The product of multiplying an integer by itself is the square of a number. Squaring is 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 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 (-81)², 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: (-81)²
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: (-81)² = (-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 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.
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
Sarah is planning to replace the tiles on her square kitchen floor of length 81 feet. The cost to replace a foot is 10 dollars. Then how much will it cost to replace the full floor?
The length of the floor = 81 feet
The cost to replace 1 square foot of floor = 10 dollars.
To find the total cost to replace, we find the area of the floor,
Area of the floor = area of the square = a²
Here a = 81 Therefore, the area of the floor = 81² = 81 × 81 = 6561.
The cost to replace the floor = 6561 × 10 = 65610.
The total cost = 65610 dollars
Explanation
To find the cost to replace the floor, we multiply the area of the floor by the cost to replace per foot. So, the total cost is 65610 dollars.
Problem 3
Find the area of a circle whose radius is 81 meters.
The area of the circle = 20609.76 m²
Explanation
The area of a circle = πr²
Here, r = 81
Therefore, the area of the circle = π × 81² = 3.14 × 81 × 81 = 20609.76 m².
Problem 4
The area of the square is 6561 cm². Find the perimeter of the square.
The perimeter of the square is
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.
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.What is the square root of 81?
4.What are the first few multiples of 81?
5.What is the square of 80?
Important Glossaries for Square of -81.
- Imaginary unit: The imaginary unit 'i' is defined as the square root of -1. It is used to express complex numbers.
- Perfect square: A perfect square is a number that is the square of an integer. For example, 64 is a perfect square because it is 8².
- Exponent: An exponent refers to the number of times a number (the base) is multiplied by itself. In the expression a², 2 is the exponent.
- Multiplication: Multiplication is a mathematical operation used to calculate the total of one number multiplied by another.
- Square root: The square root is the inverse operation of squaring a number. It is a number that, when multiplied by itself, gives the original number.
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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
: He loves to play the quiz with kids through algebra to make kids love it.
