113 LearnersLast updated on May 26th, 2025
Square of 420
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 420.
What is the Square of 420
The square of a number is the product of the number itself. The square of 420 is 420 × 420. The square of a number always ends in 0, 1, 4, 5, 6, or 9. We write it in math as 420², where 420 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 420 is 420 × 420 = 176400.
Square of 420 in exponential form: 420²
Square of 420 in arithmetic form: 420 × 420
How to Calculate the Value of Square of 420
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 420.
Step 1: Identify the number. Here, the number is 420.
Step 2: Multiplying the number by itself, we get, 420 × 420 = 176400.
The square of 420 is 176400.
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 420.
So: 420² = 420 × 420 = 176400
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 420.
Step 1: Enter the number in the calculator Enter 420 in the calculator.
Step 2: Multiply the number by itself using the multiplication button (×) That is 420 × 420
Step 3: Press the equal to button to find the answer Here, the square of 420 is 176400.
Tips and Tricks for the Square of 420: 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 420
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.
Solved Examples on Square of 420
Problem 1
Find the length of the square, where the area of the square is 176400 cm².
The area of a square = a²
So, the area of a square = 176400 cm²
So, the length = √176400 = 420.
The length of each side = 420 cm
Explanation
The length of a square is 420 cm.
Because the area is 176400 cm², the length is √176400 = 420.
Problem 2
Jack is planning to paint his square wall of length 420 feet. The cost to paint a foot is 3 dollars. Then how much will it cost to paint the full wall?
The length of the wall = 420 feet The cost to paint 1 square foot of wall = 3 dollars.
To find the total cost to paint, we find the area of the wall,
Area of the wall = area of the square = a²
Here a = 420 Therefore, the area of the wall = 420² = 420 × 420 = 176400.
The cost to paint the wall = 176400 × 3 = 529200.
The total cost = 529200 dollars
Explanation
To find the cost to paint the wall, we multiply the area of the wall by the cost to paint per foot. So, the total cost is 529200 dollars.
Problem 3
Find the area of a circle whose radius is 420 meters.
The area of the circle = 554,153.2 m²
Explanation
The area of a circle = πr²
Here, r = 420
Therefore, the area of the circle = π × 420² = 3.14 × 420 × 420 = 554,153.2 m².
Problem 4
The area of a square is 176400 cm². Find the perimeter of the square.
The perimeter of the square is 1680 cm.
Explanation
The area of the square = a²
Here, the area is 176400 cm²
The length of the side is √176400 = 420
Perimeter of the square = 4a
Here, a = 420
Therefore, the perimeter = 4 × 420 = 1680.
Problem 5
Find the square of 421.
The square of 421 is 177241.
Explanation
The square of 421 is multiplying 421 by 421.
So, the square = 421 × 421 = 177241.
FAQs on Square of 420
1.What is the square of 420?
2.What is the square root of 420?
3.Is 420 a prime number?
4.What are the first few multiples of 420?
5.What is the square of 421?
Important Glossaries for Square 420.
- Perfect square: A perfect square is a number that can be expressed as the product of an integer with itself. For example, 16 is a perfect square because 4 × 4 = 16.
- Prime number: A prime number is a natural number greater than 1 that has no divisors other than 1 and itself.
- Square: The square of a number is the result of multiplying the number by itself. For example, the square of 5 is 25.
- Exponent: An exponent refers to the number that indicates how many times a base is multiplied by itself. For example, in 2³, 3 is the exponent.
- Calculator: A calculator is a device used to perform calculations, ranging from basic arithmetic to complex mathematics.
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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.
