114 LearnersLast updated on May 26th, 2025
Square of 691
The product of multiplying an integer by itself is the square of a number. Squares are used in programming, calculating areas, and more. In this topic, we will discuss the square of 691.
What is the Square of 691
The square of a number is the product of the number itself. The square of 691 is 691 × 691. The square of a number always ends in 0, 1, 4, 5, 6, or 9. We write it in math as 691², where 691 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 691 is 691 × 691 = 477,481. Square of 691 in exponential form: 691² Square of 691 in arithmetic form: 691 × 691
How to Calculate the Value of Square of 691
The square of a number is multiplying the number by itself. 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 691. Step 1: Identify the number. Here, the number is 691. Step 2: Multiplying the number by itself, we get, 691 × 691 = 477,481. The square of 691 is 477,481.
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 691. So: 691² = 691 × 691 = 477,481.
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 691. Step 1: Enter the number in the calculator. Enter 691 in the calculator. Step 2: Multiply the number by itself using the multiplication button (×). That is 691 × 691. Step 3: Press the equal to button to find the answer. Here, the square of 691 is 477,481. Tips and Tricks for the Square of 691 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 691
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.
Mistake 2
Errors when using the formula
The formula to find the square of the number is a². Instead, students may use 691² with (6+9+1)² or (600+90+1)². 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 691
Problem 1
Find the side length of a square whose area is 477,481 cm².
The area of a square = a² So, the area of a square = 477,481 cm² So, the length = √477,481 = 691. The length of each side = 691 cm.
Explanation
The length of a square is 691 cm because the area is 477,481 cm², and the length is √477,481 = 691.
Problem 2
A farmer wants to fence a square plot with a side length of 691 feet. If the cost of fencing per foot is 5 dollars, how much will it cost to fence the entire plot?
The length of the side of the plot = 691 feet The cost to fence 1 foot = 5 dollars To find the total cost to fence, we find the perimeter of the plot, Perimeter of the plot = 4a Here a = 691 Therefore, the perimeter = 4 × 691 = 2,764. The cost to fence the plot = 2,764 × 5 = 13,820. The total cost = 13,820 dollars.
Explanation
To find the cost to fence the plot, multiply the perimeter by the cost to fence per foot. So, the total cost is 13,820 dollars.
Problem 3
Find the area of a circle whose radius is 691 meters.
The area of the circle = 1,500,626.34 m²
Explanation
The area of a circle = πr² Here, r = 691 Therefore, the area of the circle = π × 691² = 3.14 × 691 × 691 = 1,500,626.34 m².
Problem 4
The area of a square is 691² cm². Find the perimeter of the square.
The perimeter of the square is 2,764 cm.
Explanation
The area of the square = a² Here, the area is 691² cm² The length of the side is √691² = 691 Perimeter of the square = 4a Here, a = 691 Therefore, the perimeter = 4 × 691 = 2,764.
Problem 5
Find the square of 692.
The square of 692 is 478,864.
Explanation
The square of 692 is multiplying 692 by 692. So, the square = 692 × 692 = 478,864.
FAQs on Square of 691
1.What is the square of 691?
2.What is the square root of 691?
3.Is 691 a prime number?
4.What are the first few multiples of 691?
5.What is the square of 690?
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 691?
8.How do technology and digital tools in Australia support learning Algebra and Square of 691?
9.Does learning Algebra support future career opportunities for students in Australia?
Important Glossaries for Square of 691
Prime number: A number that is only divisible by 1 and itself. For example, 2, 3, 5, 7, 11, ... Exponential form: A way of writing a number using a base and an exponent. For example, 691² where 691 is the base and 2 is the exponent. Square: The result of multiplying a number by itself. For example, 691 × 691 = 477,481. Square root: The inverse operation of squaring a number. The square root of a number is a number whose square is the original number. 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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