112 LearnersLast updated on May 26th, 2025
Square of 102
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 102.
What is the Square of 102
The square of a number is the product of the number itself. The square of 102 is 102 × 102. The square of a number always ends in 0, 1, 4, 5, 6, or 9. We write it in math as 102², where 102 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 102 is 102 × 102 = 10404. Square of 102 in exponential form: 102² Square of 102 in arithmetic form: 102 × 102
How to Calculate the Value of Square of 102
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 102. Step 1: Identify the number. Here, the number is 102. Step 2: Multiplying the number by itself, we get, 102 × 102 = 10404. The square of 102 is 10404.
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 102. So: 102² = 102 × 102 = 10404
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 102. Step 1: Enter the number in the calculator Enter 102 in the calculator. Step 2: Multiply the number by itself using the multiplication button (×) That is 102 × 102 Step 3: Press the equal to button to find the answer Here, the square of 102 is 10404. Tips and Tricks for the Square of 102 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 102
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 102² with (10+2)² or (100+2)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 102
Problem 1
Find the length of the square, where the area of the square is 10404 cm².
The area of a square = a² So, the area of a square = 10404 cm² So, the length = √10404 = 102. The length of each side = 102 cm
Explanation
The length of a square is 102 cm. Because the area is 10404 cm², the length is √10404 = 102.
Problem 2
Jessica is planning to carpet her square room of length 102 feet. The cost to carpet a foot is 5 dollars. Then how much will it cost to carpet the full room?
The length of the room = 102 feet The cost to carpet 1 square foot of the room = 5 dollars. To find the total cost to carpet, we find the area of the room, Area of the room = area of the square = a² Here a = 102 Therefore, the area of the room = 102² = 102 × 102 = 10404. The cost to carpet the room = 10404 × 5 = 52020. The total cost = 52020 dollars
Explanation
To find the cost to carpet the room, we multiply the area of the room by the cost to carpet per foot. So, the total cost is 52020 dollars.
Problem 3
Find the area of a circle whose radius is 102 meters.
The area of the circle = 32685.84 m²
Explanation
The area of a circle = πr² Here, r = 102 Therefore, the area of the circle = π × 102² = 3.14 × 102 × 102 = 32685.84 m².
Problem 4
The area of the square is 10404 cm². Find the perimeter of the square.
The perimeter of the square is 408 cm
Explanation
The area of the square = a² Here, the area is 10404 cm² The length of the side is √10404 = 102 Perimeter of the square = 4a Here, a = 102 Therefore, the perimeter = 4 × 102 = 408.
Problem 5
Find the square of 103.
The square of 103 is 10609
Explanation
The square of 103 is multiplying 103 by 103. So, the square = 103 × 103 = 10609
FAQs on Square of 102
1.What is the square of 102?
2.What is the square root of 102?
3.Is 102 a perfect square?
4.What are the first few multiples of 102?
5.What is the square of 101?
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 102?
8.How do technology and digital tools in United States support learning Algebra and Square of 102?
9.Does learning Algebra support future career opportunities for students in United States?
Important Glossaries for Square 102.
Perfect square: A number that is the square of an integer. For example, 64 is a perfect square because it is 8². Exponent: An exponent indicates how many times a number is multiplied by itself. For example, in 102², 2 is the exponent. Square: The result of multiplying a number by itself. For example, 9² = 81. Square root: The square root is the inverse operation of the square. The square root of a number is a number whose square is the number itself. Multiplication: A mathematical operation where a number is added to itself a certain number of times. For example, 5 × 3 = 15.
Explore More algebra
![Important Math Links Icon]()
Previous to Square of 102
About BrightChamps in United States
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
: He loves to play the quiz with kids through algebra to make kids love it.
