116 LearnersLast updated on May 26th, 2025
Square of 683
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 683.
What is the Square of 683
The square of a number is the product of the number with itself. The square of 683 is 683 × 683. The square of a number always ends in 0, 1, 4, 5, 6, or 9. We write it in math as 683², where 683 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 683 is 683 × 683 = 466,489.
Square of 683 in exponential form: 683²
Square of 683 in arithmetic form: 683 × 683
How to Calculate the Value of Square of 683
The square of a number is found by multiplying the number by itself. 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 multiply the number by itself to find the square. The product here is the square of the number. Let’s find the square of 683.
Step 1: Identify the number. Here, the number is 683.
Step 2: Multiply the number by itself, we get, 683 × 683 = 466,489.
The square of 683 is 466,489.
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: Identify the number and substitute the value in the equation.
Here, ‘a’ is 683.
So: 683² = 683 × 683 = 466,489
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 683.
Step 1: Enter the number in the calculator. Enter 683 in the calculator.
Step 2: Multiply the number by itself using the multiplication button (×). That is 683 × 683.
Step 3: Press the equal button to find the answer. Here, the square of 683 is 466,489.
Tips and Tricks for the Square of 683
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 683
Mistakes are common among kids when doing math, especially when it comes to 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 683² with (6 + 8 + 3)² or (600 + 80 + 3)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 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 683
Problem 1
Find the length of the square, where the area of the square is 466,489 cm².
The area of a square = a²
So, the area of a square = 466,489 cm²
So, the length = √466,489 = 683.
The length of each side = 683 cm
Explanation
The length of a square is 683 cm. Because the area is 466,489 cm² the length is √466,489 = 683.
Problem 2
Lisa wants to tile her square kitchen floor of length 683 feet. The cost to tile a foot is 5 dollars. How much will it cost to tile the full floor?
The length of the kitchen floor = 683 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 = 683
Therefore, the area of the floor = 683² = 683 × 683 = 466,489.
The cost to tile the floor = 466,489 × 5 = 2,332,445.
The total cost = 2,332,445 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 2,332,445 dollars.
Problem 3
Find the area of a circle whose radius is 683 meters.
The area of the circle = 1,466,292.54 m²
Explanation
The area of a circle = πr²
Here, r = 683
Therefore, the area of the circle = π × 683²
= 3.14 × 683 × 683
= 1,466,292.54 m².
Problem 4
The area of the square is 466,489 cm². Find the perimeter of the square.
The perimeter of the square is 2,732 cm.
Explanation
The area of the square = a²
Here, the area is 466,489 cm²
The length of the side is √466,489 = 683
Perimeter of the square = 4a
Here, a = 683
Therefore, the perimeter = 4 × 683 = 2,732 cm.
Problem 5
Find the square of 684.
The square of 684 is 467,856.
Explanation
The square of 684 is multiplying 684 by 684. So, the square = 684 × 684 = 467,856.
FAQs on Square of 683
1.What is the square of 683?
2.What is the square root of 683?
3.Is 683 a prime number?
4.What are the first few multiples of 683?
5.What is the square of 682?
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 683?
8.How do technology and digital tools in United States support learning Algebra and Square of 683?
9.Does learning Algebra support future career opportunities for students in United States?
Important Glossaries for Square 683.
- Prime number: A number that is divisible only by 1 and itself. For example, 2, 3, 5, 7, 11.
- Perfect square: A number that is the square of an integer. For example, 16 is a perfect square because it is 4².
- Exponential form: The notation of a number in the form of a power. For example, 9² where 9 is the base and 2 is the exponent.
- Square root: The square root is a value that, when multiplied by itself, gives the original number. For example, the square root of 16 is ±4.
- Multiplication method: A method of finding the square of a number by multiplying the number by itself.
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Jaskaran Singh Saluja
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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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