114 LearnersLast updated on May 26th, 2025
Square of 107
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 107.
What is the Square of 107
The square of a number is the product of the number itself. The square of 107 is 107 × 107. The square of a number always ends in 0, 1, 4, 5, 6, or 9. We write it in math as 107², where 107 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 107 is 107 × 107 = 11449. Square of 107 in exponential form: 107² Square of 107 in arithmetic form: 107 × 107
How to Calculate the Value of Square of 107
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 107 Step 1: Identify the number. Here, the number is 107. Step 2: Multiplying the number by itself, we get, 107 × 107 = 11449. The square of 107 is 11449.
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 107 So: 107² = 107 × 107 = 11449
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 107. Step 1: Enter the number in the calculator Enter 107 in the calculator. Step 2: Multiply the number by itself using the multiplication button(×) That is 107 × 107 Step 3: Press the equal to button to find the answer Here, the square of 107 is 11449. Tips and Tricks for the Square of 107 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 107
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 107² with (10 + 7)² or (100 + 7)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 107
Problem 1
Find the length of the square, where the area of the square is 11449 cm².
The area of a square = a² So, the area of a square = 11449 cm² So, the length = √11449 = 107. The length of each side = 107 cm
Explanation
The length of a square is 107 cm. Because the area is 11449 cm² the length is √11449 = 107.
Problem 2
Sarah wants to install tiles on her square floor of length 107 feet. The cost to install a tile per square foot is 5 dollars. Then how much will it cost to install tiles on the full floor?
The length of the floor = 107 feet The cost to install 1 square foot of tiles = 5 dollars. To find the total cost to install, we find the area of the floor, Area of the floor = area of the square = a² Here a = 107 Therefore, the area of the floor = 107² = 107 × 107 = 11449. The cost to install tiles = 11449 × 5 = 57245. The total cost = 57245 dollars
Explanation
To find the cost to install tiles, we multiply the area of the floor by the cost to install per square foot. So, the total cost is 57245 dollars.
Problem 3
Find the area of a circle whose radius is 107 meters.
The area of the circle = 35932.15 m²
Explanation
The area of a circle = πr² Here, r = 107 Therefore, the area of the circle = π × 107² = 3.14 × 107 × 107 = 35932.15 m².
Problem 4
The area of the square is 11449 cm². Find the perimeter of the square.
The perimeter of the square is 428 cm.
Explanation
The area of the square = a² Here, the area is 11449 cm² The length of the side is √11449 = 107 Perimeter of the square = 4a Here, a = 107 Therefore, the perimeter = 4 × 107 = 428.
Problem 5
Find the square of 108.
The square of 108 is 11664
Explanation
The square of 108 is multiplying 108 by 108. So, the square = 108 × 108 = 11664
FAQs on Square of 107
1.What is the square of 107?
2.What is the square root of 107?
3.Is 107 a prime number?
4.What are the first few multiples of 107?
5.What is the square of 106?
6.How does learning Algebra help students in United States make better decisions in daily life?
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9.Does learning Algebra support future career opportunities for students in United States?
Important Glossaries for Square 107.
Prime number: A number that is only divisible by 1 and itself. For example, 2, 3, 5, 7, 11, etc. Exponential form: A mathematical expression where a number is raised to a power, e.g., 9² where 9 is the base and 2 is the exponent. Square root: The inverse operation of squaring a number. The square root of a number is a value that, when multiplied by itself, gives the original number. Perfect square: A number that is the square of an integer. For example, 121 is a perfect square because it is 11². Multiplication method: A way to find the square of a number by multiplying the number by itself.
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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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