132 LearnersLast updated on May 27th, 2025
Square of 4000
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 4000.
What is the Square of 4000
The square of a number is the product of the number with itself.
The square of 4000 is 4000 × 4000.
We write it in math as (40002), where 4000 is the base and 2 is the exponent.
The square of a positive and a negative number is always positive. For example, (52 = 25); ((-5)2 = 25).
The square of 4000 is 4000 × 4000 = 16,000,000.
Square of 4000 in exponential form: (40002)
Square of 4000 in arithmetic form: 4000 × 4000
How to Calculate the Value of Square of 4000
The square of a number is 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 (a2)
- 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 4000.
Step 1: Identify the number. Here, the number is 4000.
Step 2: Multiplying the number by itself, we get, 4000 × 4000 = 16,000,000.
The square of 4000 is 16,000,000.
Using a Formula (\(a^2\))
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 4000. So: (40002 = 4000 × 4000 = 16,000,000)
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 4000.
Step 1: Enter the number in the calculator Enter 4000 in the calculator.
Step 2: Multiply the number by itself using the multiplication button (×). That is 4000 × 4000.
Step 3: Press the equal to button to find the answer. Here, the square of 4000 is 16,000,000.
Tips and Tricks for the Square of 4000
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 4000
Mistakes are common among kids when doing math, especially when it comes to 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 the digits. To avoid this, 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 mistakenly use (3 + 7)2 or (30 + 7)2 for (40002). Students should check and use the correct formula and double-check their answers to avoid confusion.
Mistake 3
Confusing square and square root.
Not understanding the concept of squares and square roots can lead to confusion in students. To avoid this, 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 parentheses when finding the square of a number can lead to errors. So, students should understand parentheses and perform operations in the correct order to avoid errors.
Mistake 5
Not practicing regularly.
Regular practice is required to master the square of a number. Students should practice regularly to avoid errors.
Solved Examples on Square of 4000
Problem 1
Find the length of a square where the area of the square is 16,000,000 cm².
The area of a square = (a2)
So, the area of a square = 16,000,000 cm²
Therefore, the length = ( √ 16,000,000 = 4000).
The length of each side = 4000 cm
Explanation
The length of the square is 4000 cm.
Because the area is 16,000,000 cm², the length is ( √ 16,000,000 = 4000).
Problem 2
Sarah is planning to tile her square garden of length 4000 feet. The cost to tile a square foot is 10 dollars. How much will it cost to tile the entire garden?
The length of the garden = 4000 feet
The cost to tile 1 square foot of garden = 10 dollars.
To find the total cost to tile, we calculate the area of the garden.
Area of the garden = area of the square = (a2)
Here (a = 4000).
Therefore, the area of the garden = (40002 = 4000 × 4000 = 16,000,000).
The cost to tile the garden = 16,000,000 × 10 = 160,000,000.
The total cost = 160,000,000 dollars
Explanation
To find the cost to tile the garden, we multiply the area of the garden by the cost to tile per square foot.
The total cost is 160,000,000 dollars.
Problem 3
Find the area of a circle whose radius is 4000 meters.
The area of the circle = 50,265,482.46 m²
Explanation
The area of a circle = (pi r2)
Here, (r = 4000).
Therefore, the area of the circle = (pi × 40002) = (3.14 × 4000 × 4000 = 50,265,482.46) m².
Problem 4
The area of a square is 16,000,000 cm². Find the perimeter of the square.
The perimeter of the square is 16,000 cm
Explanation
The area of the square = (a2)
Here, the area is 16,000,000 cm²
The length of the side is ( √ 16,000,000 = 4000)
Perimeter of the square = 4a
Here, (a = 4000)
Therefore, the perimeter = 4 × 4000 = 16,000.
Problem 5
Find the square of 4010.
The square of 4010 is 16,080,100
Explanation
The square of 4010 is multiplying 4010 by 4010.
So, the square = 4010 × 4010 = 16,080,100
FAQs on Square of 4000
1.What is the square of 4000?
2.What is the square root of 4000?
3.What are the first few multiples of 4000?
4.What is the square of 3999?
5.Is 4000 a perfect square?
6.How does learning Algebra help students in United Arab Emirates make better decisions in daily life?
7.How can cultural or local activities in United Arab Emirates support learning Algebra topics such as Square of 4000?
8.How do technology and digital tools in United Arab Emirates support learning Algebra and Square of 4000?
9.Does learning Algebra support future career opportunities for students in United Arab Emirates?
Important Glossaries for Square of 4000
- Perfect Square: A number that is the square of an integer. For example, 16 is a perfect square because it is (42).
- Square: The result of multiplying a number by itself. For example, the square of 5 is 25.
- Exponent: The number that denotes how many times a base is multiplied by itself. In (23), 3 is the exponent.
- Multiplication: The arithmetic operation of scaling one number by another.
- Calculator: An electronic or mechanical device used for performing mathematical calculations.
Explore More algebra
![Important Math Links Icon]()
Previous to Square of 4000
About BrightChamps in United Arab Emirates
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.
