133 LearnersLast updated on May 30th, 2025
Square of 408
The product of multiplying an integer by itself is the square of a number. Squares are used in programming, calculating areas, and more. In this topic, we will discuss the square of 408.
What is the Square of 408
The square of a number is the product of the number with itself.
The square of 408 is 408 × 408.
The square of a number always ends in 0, 1, 4, 5, 6, or 9.
We write it in math as 408², where 408 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 408 is 408 × 408 = 166,464.
Square of 408 in exponential form: 408²
Square of 408 in arithmetic form: 408 × 408
How to Calculate the Value of the Square of 408
The square of a number is found by multiplying the number by itself. 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 408.
Step 1: Identify the number. Here, the number is 408
Step 2: Multiplying the number by itself, we get, 408 × 408 = 166,464.
The square of 408 is 166,464.
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 408
So: 408² = 408 × 408 = 166,464
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 408.
Step 1: Enter the number in the calculator Enter 408 in the calculator.
Step 2: Multiply the number by itself using the multiplication button (×) That is 408 × 408
Step 3: Press the equal to button to find the answer
Here, the square of 408 is 166,464.
Tips and Tricks for the Square of 408
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 408
Mistakes are common among kids when doing math, especially when 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 steps or swap 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 (40 + 8)². So students should check and use the correct formula and double-check the answers to avoid confusion.
Mistake 3
Confusing 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 errors.
Mistake 5
Not practicing regularly.
Regular practice is required to master the square of a number. So students should practice regularly to avoid errors.
Solved Examples on Square of 408
Problem 1
Find the length of a square where the area of the square is 166,464 cm².
The area of a square = a² So, the area of a square = 166,464 cm² So, the length = √166,464 = 408. The length of each side = 408 cm
Explanation
The length of a square is 408 cm because the area is 166,464 cm², and the length is √166,464 = 408.
Problem 2
Sarah is planning to tile her square patio with tiles, each side of 408 feet. The cost to tile a square foot is 5 dollars. How much will it cost to tile the entire patio?
The length of the patio = 408 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 = 408 Therefore, the area of the patio = 408² = 408 × 408 = 166,464. The cost to tile the patio = 166,464 × 5 = 832,320. The total cost = 832,320 dollars
Explanation
To find the cost to tile the patio, we multiply the area of the patio by the cost to tile per square foot.
So, the total cost is 832,320 dollars.
Problem 3
Find the area of a circle whose radius is 408 meters.
The area of the circle = 522,402.24 m²
Explanation
The area of a circle = πr²
Here, r = 408
Therefore, the area of the circle = π × 408² = 3.14 × 408 × 408 = 522,402.24 m².
Problem 4
The area of a square is 166,464 cm². Find the perimeter of the square.
The perimeter of the square is 1,632 cm
Explanation
The area of the square = a²
Here, the area is 166,464 cm²
The length of the side is √166,464 = 408
Perimeter of the square = 4a
Here, a = 408
Therefore, the perimeter = 4 × 408 = 1,632.
Problem 5
Find the square of 409.
The square of 409 is 167,281
Explanation
The square of 409 is multiplying 409 by 409.
So, the square = 409 × 409 = 167,281
FAQs on Square of 408
1.What is the square of 408?
2.What is the square root of 408?
3.Is 408 a prime number?
4.What are the first few multiples of 408?
5.What is the square of 407?
6.How does learning Algebra help students in Singapore make better decisions in daily life?
7.How can cultural or local activities in Singapore support learning Algebra topics such as Square of 408?
8.How do technology and digital tools in Singapore support learning Algebra and Square of 408?
9.Does learning Algebra support future career opportunities for students in Singapore?
Important Glossaries for Square 408.
- Square: The result of multiplying a number by itself.
- Perfect Square: A number that is the square of an integer.
- Prime Number: A number greater than 1 with no divisors other than 1 and itself.
- Exponential Form: A way of expressing a number using a base and an exponent.
- Square Root: A value that, when multiplied by itself, gives the original number.
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About BrightChamps in Singapore
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.
