100 LearnersLast updated on May 26th, 2025
Square of 677
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 677.
What is the Square of 677
The square of a number is the product of the number itself. The square of 677 is 677 × 677. The square of a number always ends in 0, 1, 4, 5, 6, or 9. We write it in math as 677², where 677 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 677 is 677 × 677 = 458,329.
Square of 677 in exponential form: 677²
Square of 677 in arithmetic form: 677 × 677
How to Calculate the Value of Square of 677
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 677.
Step 1: Identify the number. Here, the number is 677.
Step 2: Multiplying the number by itself, we get, 677 × 677 = 458,329.
The square of 677 is 458,329.
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 677.
So: 677² = 677 × 677 = 458,329
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 677.
Step 1: Enter the number in the calculator Enter 677 in the calculator.
Step 2: Multiply the number by itself using the multiplication button (×) That is 677 × 677
Step 3: Press the equal to button to find the answer Here, the square of 677 is 458,329.
Tips and Tricks for the Square of 677
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 677
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.
Solved Examples on Square of 677
Problem 1
A square garden has an area of 458,329 square meters. Find the length of one side of the garden.
The area of a square = a²
So, the area of a square = 458,329 m²
So, the length = √458,329 = 677.
The length of each side = 677 meters
Explanation
The length of a square garden is 677 meters. Because the area is 458,329 m², the length is √458,329 = 677.
Problem 2
Sarah wants to tile her square patio, which has a side length of 677 feet. If the cost to tile one square foot is 2 dollars, how much will it cost to tile the entire patio?
The length of the patio = 677 feet
The cost to tile 1 square foot of the patio = 2 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 = 677
Therefore, the area of the patio = 677² = 677 × 677 = 458,329.
The cost to tile the patio = 458,329 × 2 = 916,658.
The total cost = 916,658 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 916,658 dollars.
Problem 3
Find the area of a circle whose radius is 677 meters.
The area of the circle = 1,439,822.06 m²
Explanation
The area of a circle = πr²
Here, r = 677
Therefore, the area of the circle = π × 677²
= 3.14 × 677 × 677
= 1,439,822.06 m².
Problem 4
The area of a square is 458,329 cm². Find the perimeter of the square.
The perimeter of the square is 2,708 cm.
Explanation
The area of the square = a²
Here, the area is 458,329 cm²
The length of the side is √458,329 = 677
Perimeter of the square = 4a
Here, a = 677 x
Therefore, the perimeter = 4 × 677 = 2,708.
Problem 5
Find the square of 678.
The square of 678 is 459,684.
Explanation
The square of 678 is multiplying 678 by 678.
So, the square = 678 × 678 = 459,684
FAQs on Square of 677
1.What is the square of 677?
2.What is the square root of 677?
3.Is 677 a prime number?
4.What are the first few multiples of 677?
5.What is the square of 676?
6.How does learning Algebra help students in United States make better decisions in daily life?
7.How can cultural or local activities in United States support learning Algebra topics such as Square of 677?
8.How do technology and digital tools in United States support learning Algebra and Square of 677?
9.Does learning Algebra support future career opportunities for students in United States?
Important Glossaries for Square of 677.
- Prime number: A number that is only divisible by 1 and itself. For example, 677 is a prime number.
- Exponential form: A way of writing numbers using a base and an exponent. For example, 677² where 677 is the base and 2 is the exponent.
- Square: The result of multiplying a number by itself. For example, the square of 5 is 25.
- Square root: The number that, when multiplied by itself, gives the original number. For example, the square root of 25 is 5.
- Perfect square: A number that is the square of an integer. For example, 144 is a perfect square because it is 12².
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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.
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