114 LearnersLast updated on May 26th, 2025
Square of 108
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 108.
What is the Square of 108
The square of a number is the product of the number itself. The square of 108 is 108 × 108. The square of a number always ends in 0, 1, 4, 5, 6, or 9. We write it in math as 108², where 108 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 108 is 108 × 108 = 11664. Square of 108 in exponential form: 108² Square of 108 in arithmetic form: 108 × 108
How to Calculate the Value of Square of 108
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 108 Step 1: Identify the number. Here, the number is 108 Step 2: Multiplying the number by itself, we get, 108 × 108 = 11664. The square of 108 is 11664.
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 108 So: 108² = 108 × 108 = 11664
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 108. Step 1: Enter the number in the calculator Enter 108 in the calculator. Step 2: Multiply the number by itself using the multiplication button(×) That is 108 × 108 Step 3: Press the equal to button to find the answer Here, the square of 108 is 11664. Tips and Tricks for the Square of 108 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 108
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 108² with (10 + 8)² or (100 + 8)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 108
Problem 1
Find the length of the square, where the area of the square is 11664 cm².
The area of a square = a² So, the area of a square = 11664 cm² So, the length = √11664 = 108. The length of each side = 108 cm
Explanation
The length of a square is 108 cm. Because the area is 11664 cm² the length is √11664 = 108.
Problem 2
Anna wants to tile her square patio of length 108 feet. The cost to tile a square foot is 5 dollars. Then how much will it cost to tile the full patio?
The length of the patio = 108 feet The cost to tile 1 square foot of patio = 5 dollars. To find the total cost to tile, we find the area of the patio, Area of the patio = area of the square = a² Here a = 108 Therefore, the area of the patio = 108² = 108 × 108 = 11664. The cost to tile the patio = 11664 × 5 = 58320. The total cost = 58320 dollars
Explanation
To find the cost to tile the patio, we multiply the area of the patio by the cost to tile per foot. So, the total cost is 58320 dollars.
Problem 3
Find the area of a circle whose radius is 108 meters.
The area of the circle = 36605.76 m²
Explanation
The area of a circle = πr² Here, r = 108 Therefore, the area of the circle = π × 108² = 3.14 × 108 × 108 = 36605.76 m².
Problem 4
The area of the square is 11664 cm². Find the perimeter of the square.
The perimeter of the square is 432 cm.
Explanation
The area of the square = a² Here, the area is 11664 cm² The length of the side is √11664 = 108 Perimeter of the square = 4a Here, a = 108 Therefore, the perimeter = 4 × 108 = 432.
Problem 5
Find the square of 109.
The square of 109 is 11881
Explanation
The square of 109 is multiplying 109 by 109. So, the square = 109 × 109 = 11881
FAQs on Square of 108
1.What is the square of 108?
2.What is the square root of 108?
3.Is 108 a prime number?
4.What are the first few multiples of 108?
5.What is the square of 107?
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 108?
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9.Does learning Algebra support future career opportunities for students in United States?
Important Glossaries for Square of 108.
Perfect square: A number that is the square of an integer. For example, 11664 is a perfect square because it is 108². Even number: An integer that is divisible by 2. For example, 108 is an even number. Prime number: A number greater than 1 with no positive divisors other than 1 and itself. For example, 37 is a prime number. Exponential form: A way of expressing numbers as a base raised to a power. For example, 108² is in exponential form. Square root: The value that, when multiplied by itself, gives the original number. For example, the square root of 11664 is 108.
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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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