130 LearnersLast updated on May 29th, 2025
Square of 1681
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 1681.
What is the Square of 1681
The square of a number is the product of the number itself.
The square of 1681 is 1681 × 1681.
The square of a number always ends in 0, 1, 4, 5, 6, or 9.
We write it in math as 1681², where 1681 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 1681 is 1681 × 1681 = 2,822,761.
Square of 1681 in exponential form: 1681²
Square of 1681 in arithmetic form: 1681 × 1681
How to Calculate the Value of Square of 1681
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 (a2)
- 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 1681.
Step 1: Identify the number. Here, the number is 1681.
Step 2: Multiplying the number by itself, we get, 1681 × 1681 = 2,822,761.
The square of 1681 is 2,822,761.
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 1681
So: 1681² = 1681 × 1681 = 2,822,761
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 1681.
Step 1: Enter the number in the calculator. Enter 1681 in the calculator.
Step 2: Multiply the number by itself using the multiplication button(×). That is 1681 × 1681
Step 3: Press the equal to button to find the answer. Here, the square of 1681 is 2,822,761.
Tips and Tricks for the Square of 1681
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 1681
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 when using the formula.
The formula to find the square of the number is a². Instead, students may use 1681² with (1000+681)² or (1000+680+1)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 1681
Problem 1
Emily is planning a garden and wants the area to be a perfect square of 1681 m². What will be the length of each side of the garden?
The area of a square = a²
So, the area of a square = 1681 m²
So, the length = √1681 = 41.
The length of each side = 41 m
Explanation
The length of a square is 41 m.
Because the area is 1681 m², the length is √1681 = 41.
Problem 2
A square picture frame has a side length of 41 cm. The cost to add a border around the frame is $2 per cm. How much will it cost to add the border around the entire frame?
The length of the frame = 41 cm
The cost to add a border around 1 cm of the frame = $2.
To find the total cost to add the border, we find the perimeter of the frame, Perimeter of the frame = 4a
Here a = 41
Therefore, the perimeter = 4 × 41 = 164.
The cost to add the border = 164 × 2 = $328.
The total cost = $328
Explanation
To find the cost to add the border around the frame, we multiply the perimeter of the frame by the cost per cm. So, the total cost is $328.
Problem 3
Find the area of a circle whose diameter is 82 meters.
The area of the circle = 5,281.92 m²
Explanation
The area of a circle = πr²
Here, the diameter is 82 meters, so the radius r = 41 meters.
Therefore, the area of the circle = π × 41² = 3.14 × 41 × 41 = 5,281.92 m².
Problem 4
The area of the square is 2,822,761 cm². Find the perimeter of the square.
The perimeter of the square is
Explanation
The area of the square = a²
Here, the area is 2,822,761 cm²
The length of the side is √2,822,761 = 1681
Perimeter of the square = 4a
Here, a = 1681
Therefore, the perimeter = 4 × 1681 = 6,724.
Problem 5
Find the square of 42.
The square of 42 is 1,764.
Explanation
The square of 42 is multiplying 42 by 42.
So, the square = 42 × 42 = 1,764.
FAQs on Square of 1681
1.What is the square of 1681?
2.What is the square root of 1681?
3.Is 41 a prime number?
4.What are the first few multiples of 41?
5.What is the square of 40?
6.How does learning Algebra help students in Philippines make better decisions in daily life?
7.How can cultural or local activities in Philippines support learning Algebra topics such as Square of 1681?
8.How do technology and digital tools in Philippines support learning Algebra and Square of 1681?
9.Does learning Algebra support future career opportunities for students in Philippines?
Important Glossaries for Square of 1681.
- Prime number: Any number that is only divisible by 1 and the number itself is a prime number. For example, 2, 3, 5, 7, 11, 13, 17, 19, 23, 29, 31, 37, 41, etc.
- 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.
- Perfect square: A number that is the square of an integer. For example, 1, 4, 9, 16, 25, etc.
- Perimeter: The total distance around the edge of a two-dimensional shape. For example, the perimeter of a square is 4 times the length of one side.
- Area: The measure of the space inside a two-dimensional shape. For example, the area of a square is the square of the length of its side.
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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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