136 LearnersLast updated on May 30th, 2025
Square of 400
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 400.
What is the Square of 400
The square of a number is the product of the number itself.
The square of 400 is 400 × 400.
The square of a number ends in 0, 1, 4, 5, 6, or 9.
We write it in math as 400², where 400 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 400 is 400 × 400 = 160,000.
Square of 400 in exponential form: 400²
Square of 400 in arithmetic form: 400 × 400
How to Calculate the Value of the Square of 400
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 400.
Step 1: Identify the number. Here, the number is 400.
Step 2: Multiplying the number by itself, we get, 400 × 400 = 160,000.
The square of 400 is 160,000.
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 400
So: 400² = 400 × 400 = 160,000
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 400.
Step 1: Enter the number in the calculator Enter 400 in the calculator.
Step 2: Multiply the number by itself using the multiplication button(×) That is 400 × 400
Step 3: Press the equal to button to find the answer
Here, the square of 400 is 160,000.
Tips and Tricks for the Square of 400
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 400
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 use 400² with (4 + 0)² or (40 + 0)². So students should check and use the correct formula and double-check the answers to avoid all the 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 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 400
Problem 1
Find the length of the square, where the area of the square is 160,000 cm².
The area of a square = a² So, the area of a square = 160,000 cm² So, the length = √160,000 = 400. The length of each side = 400 cm
Explanation
The length of a square is 400 cm.
Because the area is 160,000 cm², the length is √160,000 = 400.
Problem 2
Sarah is planning to carpet her square living room of length 400 feet. The cost to carpet a foot is 2 dollars. Then how much will it cost to carpet the full room?
The length of the room = 400 feet The cost to carpet 1 square foot of room = 2 dollars. To find the total cost to carpet, we find the area of the room, Area of the room = area of the square = a² Here a = 400 Therefore, the area of the room = 400² = 400 × 400 = 160,000. The cost to carpet the room = 160,000 × 2 = 320,000. The total cost = 320,000 dollars
Explanation
To find the cost to carpet the room, we multiply the area of the room by the cost to carpet per foot.
So, the total cost is 320,000 dollars.
Problem 3
Find the area of a circle whose radius is 400 meters.
The area of the circle = 502,400 m²
Explanation
The area of a circle = πr²
Here, r = 400
Therefore, the area of the circle = π × 400² = 3.14 × 400 × 400 = 502,400 m².
Problem 4
The area of the square is 160,000 cm². Find the perimeter of the square.
The perimeter of the square is
Explanation
The area of the square = a²
Here, the area is 160,000 cm²
The length of the side is √160,000 = 400
Perimeter of the square = 4a
Here, a = 400
Therefore, the perimeter = 4 × 400 = 1,600.
Problem 5
Find the square of 401.
The square of 401 is 160,801
Explanation
The square of 401 is multiplying 401 by 401.
So, the square = 401 × 401 = 160,801
FAQs on Square of 400
1.What is the square of 400?
2.What is the square root of 400?
3.Is 400 a prime number?
4.What are the first few multiples of 400?
5.What is the square of 399?
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 400?
8.How do technology and digital tools in United States support learning Algebra and Square of 400?
9.Does learning Algebra support future career opportunities for students in United States?
Important Glossaries for Square 400.
- Even number: A number divisible by 2 without a remainder, such as 2, 4, 6, 8, etc.
- Perfect square: A number that is the square of an integer. For example, 400 is a perfect square of 20.
- Exponent: A number that shows how many times to use the base number in a multiplication. For example, in 400², 2 is the exponent.
- Area: The measure of the extent of a two-dimensional surface or shape.
- Prime number: A number greater than 1 that has no positive divisors other than 1 and itself.
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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
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