100 LearnersLast updated on May 26th, 2025
Square of 678
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 678.
What is the Square of 678
The square of a number is the product of the number itself. The square of 678 is 678 × 678. The square of a number always ends in 0, 1, 4, 5, 6, or 9. We write it in math as 678², where 678 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 678 is 678 × 678 = 459,684.
Square of 678 in exponential form: 678²
Square of 678 in arithmetic form: 678 × 678
How to Calculate the Value of Square of 678
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 678.
Step 1: Identify the number. Here, the number is 678.
Step 2: Multiplying the number by itself, we get, 678 × 678 = 459,684.
The square of 678 is 459,684.
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 678
So: 678² = 678 × 678 = 459,684
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 678.
Step 1: Enter the number in the calculator Enter 678 in the calculator.
Step 2: Multiply the number by itself using the multiplication button (×) That is 678 × 678
Step 3: Press the equal to button to find the answer Here, the square of 678 is 459,684.
Tips and Tricks for the Square of 678
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 678
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 678
Problem 1
Find the length of a square where the area of the square is 459,684 cm².
The area of a square = a²
So, the area of a square = 459,684 cm²
So, the length = √459,684 = 678.
The length of each side = 678 cm
Explanation
The length of a square is 678 cm. Because the area is 459,684 cm², the length is √459,684 = 678.
Problem 2
Sarah is planning to tile her square patio of length 678 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 = 678 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 = 678
Therefore, the area of the patio = 678² = 678 × 678 = 459,684.
The cost to tile the patio = 459,684 × 5 = 2,298,420.
The total cost = 2,298,420 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 2,298,420 dollars.
Problem 3
Find the area of a circle whose radius is 678 meters.
The area of the circle = 1,444,797.24 m²
Explanation
The area of a circle = πr²
Here, r = 678
Therefore, the area of the circle = π × 678²
= 3.14 × 678 × 678
= 1,444,797.24 m².
Problem 4
The area of the square is 459,684 cm². Find the perimeter of the square.
The perimeter of the square is 2712 cm.
Explanation
The area of the square = a²
Here, the area is 459,684 cm²
The length of the side is √459,684 = 678
Perimeter of the square = 4a
Here, a = 678
Therefore, the perimeter = 4 × 678 = 2712.
Problem 5
Find the square of 679.
The square of 679 is 461,041.
Explanation
The square of 679 is multiplying 679 by 679. So, the square = 679 × 679 = 461,041.
FAQs on Square of 678
1.What is the square of 678?
2.What is the square root of 678?
3.Is 678 a prime number?
4.What are the first few multiples of 678?
5.What is the square of 679?
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 678?
8.How do technology and digital tools in United Kingdom support learning Algebra and Square of 678?
9.Does learning Algebra support future career opportunities for students in United Kingdom?
Important Glossaries for Square 678.
- Perfect square: A number that is the square of an integer. For example, 144 is a perfect square because it is 12².
- Exponential form: Exponential form is the way of writing a number in the form of a power. For example, 9² where 9 is the base and 2 is the power.
- Square root: The square root is the inverse operation of the square. The square root of a number is a number whose square is the number itself.
- Even number: A number divisible by 2 without a remainder. For example, 2, 4, 6, 8, etc.
- Prime number: A number that is only divisible by 1 and itself. For example, 2, 3, 5, etc.
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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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