131 LearnersLast updated on May 30th, 2025
Square of 398
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 398.
What is the Square of 398
The square of a number is the product of the number itself.
The square of 398 is 398 × 398.
The square of a number always ends in 0, 1, 4, 5, 6, or 9.
We write it in math as 398², where 398 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 398 is 398 × 398 = 158,404.
Square of 398 in exponential form: 398²
Square of 398 in arithmetic form: 398 × 398
How to Calculate the Value of Square of 398
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 398
Step 1: Identify the number. Here, the number is 398
Step 2: Multiplying the number by itself, we get, 398 × 398 = 158,404.
The square of 398 is 158,404.
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 398
So: 398² = 398 × 398 = 158,404
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 398.
Step 1: Enter the number in the calculator Enter 398 in the calculator.
Step 2: Multiply the number by itself using the multiplication button (×) That is 398 × 398
Step 3: Press the equal to button to find the answer
Here, the square of 398 is 158,404.
Tips and Tricks for the Square of 398
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 398
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 398² with (3 + 9 + 8)² or (300 + 98)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 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 398
Problem 1
Find the length of the square, where the area of the square is 158,404 cm².
The area of a square = a² So, the area of a square = 158,404 cm² So, the length = √158,404 = 398. The length of each side = 398 cm
Explanation
The length of a square is 398 cm.
Because the area is 158,404 cm² the length is √158,404 = 398.
Problem 2
Sarah wants to cover her square garden of length 398 feet with tiles. Each tile costs 5 dollars. How much will she spend on tiles for the entire garden?
The length of the garden = 398 feet The cost to cover 1 square foot of the garden = 5 dollars. To find the total cost to cover the garden, we find the area of the garden, Area of the garden = area of the square = a² Here a = 398 Therefore, the area of the garden = 398² = 398 × 398 = 158,404. The cost to cover the garden = 158,404 × 5 = 792,020. The total cost = 792,020 dollars
Explanation
To find the cost to cover the garden, we multiply the area of the garden by the cost to cover per foot.
So, the total cost is 792,020 dollars.
Problem 3
Find the area of a circle whose radius is 398 meters.
The area of the circle = 497,089.72 m²
Explanation
The area of a circle = πr²
Here, r = 398
Therefore, the area of the circle = π × 398² = 3.14 × 398 × 398 = 497,089.72 m².
Problem 4
The area of the square is 158,404 cm². Find the perimeter of the square.
The perimeter of the square is 1,592 cm
Explanation
The area of the square = a²
Here, the area is 158,404 cm²
The length of the side is √158,404 = 398
Perimeter of the square = 4a
Here, a = 398
Therefore, the perimeter = 4 × 398 = 1,592.
Problem 5
Find the square of 399.
The square of 399 is 159,201
Explanation
The square of 399 is multiplying 399 by 399.
So, the square = 399 × 399 = 159,201
FAQs on Square of 398
1.What is the square of 398?
2.What is the square root of 398?
3.Is 398 a prime number?
4.What are the first few multiples of 398?
5.What is the square of 400?
6.How does learning Algebra help students in Qatar make better decisions in daily life?
7.How can cultural or local activities in Qatar support learning Algebra topics such as Square of 398?
8.How do technology and digital tools in Qatar support learning Algebra and Square of 398?
9.Does learning Algebra support future career opportunities for students in Qatar?
Important Glossaries for Square 398.
- Prime number: Any number that is only divisible by 1 and the number itself is a prime number. For example, 2, 3, 5, 7, 11, …
- Exponential form: Exponential form is the way of writing a number in the form of a power. For example, 9² where 9 is the base and 2 is the power.
- 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.
- Perfect square: A perfect square is a number that is the square of an integer. For example, 36 is a perfect square because it is 6².
- Multiplication method: A method to find the square of a number by multiplying the number by itself. For example, 4 × 4 = 16.
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About BrightChamps in Qatar
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.
