140 LearnersLast updated on May 30th, 2025
Square of 123
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 123.
What is the Square of 123
The square of a number is the product of the number itself.
The square of 123 is 123 × 123.
The square of a number always ends in 0, 1, 4, 5, 6, or 9.
We write it in math as 123², where 123 is the base and 2 is the exponent.
The square of a positive and a negative number is always positive. For example, 5² = 25; (-5)² = 25.
The square of 123 is 123 × 123 = 15129.
Square of 123 in exponential form: 123²
Square of 123 in arithmetic form: 123 × 123
How to Calculate the Value of Square of 123
The square of a number is found by 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 multiply the number by itself to find the square. The product here is the square of the number. Let’s find the square of 123.
Step 1: Identify the number. Here, the number is 123.
Step 2: Multiplying the number by itself, we get, 123 × 123 = 15129.
The square of 123 is 15129.
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 123. So: 123² = 123 × 123 = 15129
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 123.
Step 1: Enter the number in the calculator. Enter 123 in the calculator.
Step 2: Multiply the number by itself using the multiplication button (×). That is 123 × 123
Step 3: Press the equal to button to find the answer. Here, the square of 123 is 15129.
Tips and Tricks for the Square of 123
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 123
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 incorrectly use (1+2+3)² or (100+20+3)². So students should check and use the correct formula and double-check the answers to avoid all confusion.
Mistake 3
Confusing square with 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 with 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 errors.
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 123
Problem 1
Find the length of a square, where the area of the square is 15129 cm².
The area of a square = a²
So, the area of a square = 15129 cm²
So, the length = √15129 = 123.
The length of each side = 123 cm
Explanation
The length of a square is 123 cm. Because the area is 15129 cm², the length is √15129 = 123.
Problem 2
Alice is planning to tile her square garden of length 123 feet. The cost to tile a square foot is 5 dollars. How much will it cost to tile the entire garden?
The length of the garden = 123 feet
The cost to tile 1 square foot of the garden = 5 dollars.
To find the total cost to tile, we find the area of the garden,
Area of the garden = area of the square = a²
Here a = 123
Therefore, the area of the garden = 123² = 123 × 123 = 15129.
The cost to tile the garden = 15129 × 5 = 75645.
The total cost = 75645 dollars
Explanation
To find the cost to tile the garden, we multiply the area of the garden by the cost to tile per foot. So, the total cost is 75645 dollars.
Problem 3
Find the area of a circle whose radius is 123 meters.
The area of the circle = 47529.29 m²
Explanation
The area of a circle = πr²
Here, r = 123
Therefore, the area of the circle = π × 123² = 3.14 × 123 × 123 = 47529.29 m².
Problem 4
The area of a square is 15129 cm². Find the perimeter of the square.
The perimeter of the square is 492 cm.
Explanation
The area of the square = a²
Here, the area is 15129 cm²
The length of the side is √15129 = 123
Perimeter of the square = 4a Here, a = 123
Therefore, the perimeter = 4 × 123 = 492.
Problem 5
Find the square of 124.
The square of 124 is 15376.
Explanation
The square of 124 is multiplying 124 by 124.
So, the square = 124 × 124 = 15376.
FAQs on Square of 123
1.What is the square of 123?
2.What is the square root of 123?
3.Is 123 a prime number?
4.What are the first few multiples of 123?
5.What is the square of 122?
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 123?
8.How do technology and digital tools in Philippines support learning Algebra and Square of 123?
9.Does learning Algebra support future career opportunities for students in Philippines?
Important Glossaries for Square 123.
- Prime number: A number that is only divisible by 1 and itself. Examples include 2, 3, 5, 7, etc.
- Exponential form: Writing a number as a base raised to a power. For example, 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, 36 is a perfect square because it is 6².
- Even number: Any integer that is divisible by 2 without a remainder, such as 2, 4, 6, etc.
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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
: He loves to play the quiz with kids through algebra to make kids love it.
