111 LearnersLast updated on May 26th, 2025
Square of 642
The product of multiplying an integer by itself is the square of a number. The square is used in programming, calculating areas, and so on. In this topic, we will discuss the square of 642.
What is the Square of 642
The square of a number is the product of the number itself. The square of 642 is 642 × 642. The square of a number always ends in 0, 1, 4, 5, 6, or 9. We write it in math as 642², where 642 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 642 is 642 × 642 = 412,164.
Square of 642 in exponential form: 642²
Square of 642 in arithmetic form: 642 × 642
How to Calculate the Value of Square of 642
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 642
Step 1: Identify the number. Here, the number is 642
Step 2: Multiplying the number by itself, we get, 642 × 642 = 412,164.
The square of 642 is 412,164.
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 642 So: 642² = 642 × 642 = 412,164
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 642.
Step 1: Enter the number in the calculator Enter 642 in the calculator.
Step 2: Multiply the number by itself using the multiplication button (×) That is 642 × 642
Step 3: Press the equal to button to find the answer Here, the square of 642 is 412,164.
Tips and Tricks for the Square of 642
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 642
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 642
Problem 1
Find the length of a square, where the area of the square is 412,164 cm².
The area of a square = a²
So, the area of a square = 412,164 cm²
So, the length = √412,164 = 642.
The length of each side = 642 cm
Explanation
The length of a square is 642 cm.
Because the area is 412,164 cm², the length is √412,164 = 642.
Problem 2
Jessica is planning to tile her square garden of length 642 feet. The cost to tile a foot is 5 dollars. Then how much will it cost to tile the full garden?
The length of the garden = 642 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 = 642 Therefore, the area of the garden = 642² = 642 × 642 = 412,164. The cost to tile the garden = 412,164 × 5 = 2,060,820. The total cost = 2,060,820 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 2,060,820 dollars.
Problem 3
Find the area of a circle whose radius is 642 meters.
The area of the circle = 1,295,419.44 m²
Explanation
The area of a circle = πr²
Here, r = 642
Therefore, the area of the circle = π × 642² = 3.14 × 642 × 642 = 1,295,419.44 m².
Problem 4
The area of the square is 412,164 cm². Find the perimeter of the square.
The perimeter of the square is
Explanation
The area of the square = a²
Here, the area is 412,164 cm²
The length of the side is √412,164 = 642
Perimeter of the square = 4a
Here, a = 642
Therefore, the perimeter = 4 × 642 = 2,568.
Problem 5
Find the square of 643.
The square of 643 is 413,449
Explanation
The square of 643 is multiplying 643 by 643.
So, the square = 643 × 643 = 413,449
FAQs on Square of 642
1.What is the square of 642?
2.What is the square root of 642?
3.Is 642 a prime number?
4.What are the first few multiples of 642?
5.What is the square of 640?
Important Glossaries for Square 642.
- Perfect square: A number that is the square of an integer. For example, 412,164 is a perfect square because it is 642².
- Exponent: The power to which a number is raised, indicating repeated multiplication. For example, in 642², 2 is the exponent.
- Square root: The number which, when multiplied by itself, gives the original number. For example, the square root of 412,164 is 642.
- Prime number: A number greater than 1 with no divisors other than 1 and itself. For example, 7 is a prime number.
- Multiplication: A mathematical operation where a number is added to itself a certain number of times. For example, 642 × 642 is a multiplication operation to find the square.
Explore More algebra
Previous to Square of 642
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.
