117 LearnersLast updated on May 26th, 2025
Square of 689
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 689.
What is the Square of 689
The square of a number is the product of the number itself. The square of 689 is 689 × 689. The square of a number always ends in 0, 1, 4, 5, 6, or 9. We write it in math as 689², where 689 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 689 is 689 × 689 = 474,721.
Square of 689 in exponential form: 689²
Square of 689 in arithmetic form: 689 × 689
How to Calculate the Value of Square of 689
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 689
Step 1: Identify the number. Here, the number is 689
Step 2: Multiplying the number by itself, we get, 689 × 689 = 474,721.
The square of 689 is 474,721.
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 689
So: 689² = 689 × 689 = 474,721
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 689.
Step 1: Enter the number in the calculator Enter 689 in the calculator.
Step 2: Multiply the number by itself using the multiplication button (×) That is 689 × 689
Step 3: Press the equal to button to find the answer Here, the square of 689 is 474,721.
Tips and Tricks for the Square of 689
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 689
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 689² with (600 + 89)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.
Solved Examples on Square of 689
Problem 1
Find the length of the square, where the area of the square is 474,721 cm².
The area of a square = a²
So, the area of a square = 474,721 cm²
So, the length = √474,721 = 689.
The length of each side = 689 cm
Explanation
The length of a square is 689 cm. Because the area is 474,721 cm², the length is √474,721 = 689.
Problem 2
Sarah is planning to paint her square wall of length 689 feet. The cost to paint a foot is 3 dollars. Then how much will it cost to paint the full wall?
The length of the wall = 689 feet
The cost to paint 1 square foot of wall = 3 dollars.
To find the total cost to paint, we find the area of the wall,
Area of the wall = area of the square = a²
Here a = 689
Therefore, the area of the wall = 689² = 689 × 689 = 474,721.
The cost to paint the wall = 474,721 × 3 = 1,424,163.
The total cost = 1,424,163 dollars
Explanation
To find the cost to paint the wall, we multiply the area of the wall by the cost to paint per foot. So, the total cost is 1,424,163 dollars.
Problem 3
Find the area of a circle whose radius is 689 meters.
The area of the circle = 1,491,562.51 m²
Explanation
The area of a circle = πr²
Here, r = 689
Therefore, the area of the circle = π × 689²
= 3.14 × 689 × 689
= 1,491,562.51 m².
Problem 4
The area of a square is 474,721 cm². Find the perimeter of the square.
The perimeter of the square is 2,756 cm.
Explanation
The area of the square = a²
Here, the area is 474,721 cm²
The length of the side is √474,721 = 689
Perimeter of the square = 4a
Here, a = 689
Therefore, the perimeter = 4 × 689 = 2,756 cm.
Problem 5
Find the square of 690.
The square of 690 is 476,100.
Explanation
The square of 690 is multiplying 690 by 690. So, the square = 690 × 690 = 476,100
FAQs on Square of 689
1.What is the square of 689?
2.What is the square root of 689?
3.Is 689 a prime number?
4.What are the first few multiples of 689?
5.What is the square of 688?
6.How does learning Algebra help students in Australia make better decisions in daily life?
7.How can cultural or local activities in Australia support learning Algebra topics such as Square of 689?
8.How do technology and digital tools in Australia support learning Algebra and Square of 689?
9.Does learning Algebra support future career opportunities for students in Australia?
Important Glossaries for Square of 689
- Perfect square: A number that is the square of an integer. For example, 1, 4, 9, 16.
- Exponentiation: The operation of raising one number to the power of another. For example, 2³ = 2 × 2 × 2.
- Multiplication: The arithmetic operation of scaling one number by another. For example, 4 × 3 = 12.
- Prime number: A number greater than 1 that has no positive divisors other than 1 and itself. For example, 2, 3, 5, 7.
- Square root: The number that produces a specified quantity when multiplied by itself. For example, √9 = 3.
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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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