136 LearnersLast updated on May 26th, 2025
Square of 864
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 the topic, we will discuss the square of 864.
What is the Square of 864
The square of a number is the product of the number itself. The square of 864 is 864 × 864. The square of a number always ends in 0, 1, 4, 5, 6, or 9. We write it in math as 864², where 864 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 864 is 864 × 864 = 746,496.
Square of 864 in exponential form: 864²
Square of 864 in arithmetic form: 864 × 864
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How to Calculate the Value of Square of 864
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 864
Step 1: Identify the number. Here, the number is 864
Step 2: Multiplying the number by itself, we get, 864 × 864 = 746,496.
The square of 864 is 746,496.
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 864 So: 864² = 864 × 864 = 746,496
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 864.
Step 1: Enter the number in the calculator Enter 864 in the calculator.
Step 2: Multiply the number by itself using the multiplication button(×) That is 864 × 864
Step 3: Press the equal to button to find the answer Here, the square of 864 is 746,496.
Tips and Tricks for the Square of 864
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 864
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 86²4 with (8+6+4)² or (800+60+4)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 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.
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Solved Examples on Square of 864
Problem 1
Find the length of the square, where the area of the square is 746,496 cm².
The area of a square = a²
So, the area of a square = 746,496 cm²
So, the length = √746,496 = 864.
The length of each side = 864 cm
Explanation
The length of a square is 864 cm.
Because the area is 746,496 cm² the length is √746,496 = 864.
Problem 2
Anna is planning to tile her square floor of length 864 feet. The cost to tile a foot is 5 dollars. Then how much will it cost to tile the full floor?
The length of the floor = 864 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 = 864
Therefore, the area of the floor = 864² = 864 × 864 = 746,496.
The cost to tile the floor = 746,496 × 5 = 3,732,480.
The total cost = 3,732,480 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 3,732,480 dollars.
Problem 3
Find the area of a circle whose radius is 864 meters.
The area of the circle = 2,344,501.76 m²
Explanation
The area of a circle = πr²
Here, r = 864
Therefore, the area of the circle = π × 864² = 3.14 × 864 × 864 = 2,344,501.76 m².
Problem 4
The area of the square is 746,496 cm². Find the perimeter of the square.
The perimeter of the square is
Explanation
The area of the square = a²
Here, the area is 746,496 cm²
The length of the side is √746,496 = 864
Perimeter of the square = 4a
Here, a = 864
Therefore, the perimeter = 4 × 864 = 3,456.
Problem 5
Find the square of 865.
The square of 865 is 748,225
Explanation
The square of 865 is multiplying 865 by 865.
So, the square = 865 × 865 = 748,225
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FAQs on Square of 864
1.What is the square of 864?
2.What is the square root of 864?
3.Is 864 a perfect square?
4.What are the first few multiples of 864?
5.What is the square of 863?
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Important Glossaries for Square of 864.
- Square: The product of a number multiplied by itself.
- Perfect Square: A number that is the square of an integer.
- Square Root: The value that, when multiplied by itself, gives the original number.
- Exponential Form: A way to write numbers using a base and an exponent, such as 864².
- Area: The extent of a two-dimensional surface within a boundary, calculated for squares as side × 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.
Fun Fact
: He loves to play the quiz with kids through algebra to make kids love it.
