105 LearnersLast updated on May 26th, 2025
Square of 649
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 649.
What is the Square of 649
The square of a number is the product of the number itself. The square of 649 is 649 × 649. The square of a number always ends in 0, 1, 4, 5, 6, or 9. We write it in math as 649², where 649 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 649 is 649 × 649 = 421,201.
Square of 649 in exponential form: 649²
Square of 649 in arithmetic form: 649 × 649
How to Calculate the Value of Square of 649
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 649
Step 1: Identify the number. Here, the number is 649
Step 2: Multiplying the number by itself, we get, 649 × 649 = 421,201.
The square of 649 is 421,201.
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 649 So: 649² = 649 × 649 = 421,201
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 649.
Step 1: Enter the number in the calculator Enter 649 in the calculator.
Step 2: Multiply the number by itself using the multiplication button (×) That is 649 × 649
Step 3: Press the equal to button to find the answer Here, the square of 649 is 421,201.
Tips and Tricks for the Square of 649
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 649
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 625 is 390,625, and the square root of 390,625 is ±625.
Solved Examples on Square of 649
Problem 1
Find the length of the square, where the area of the square is 421,201 m².
The area of a square = a²
So, the area of a square = 421,201 m²
So, the length = √421,201 = 649.
The length of each side = 649 m
Explanation
The length of a square is 649 m.
Because the area is 421,201 m² the length is √421,201 = 649.
Problem 2
Anna wants to tile her square garden, which is 649 feet on each side. The cost to tile a square foot is 5 dollars. Then how much will it cost to tile the entire garden?
The length of the garden = 649 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 = 649
Therefore, the area of the garden = 649² = 649 × 649 = 421,201.
The cost to tile the garden = 421,201 × 5 = 2,106,005.
The total cost = 2,106,005 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 2,106,005 dollars.
Problem 3
Find the area of a circle whose radius is 649 meters.
The area of the circle = 1,324,214.46 m²
Explanation
The area of a circle = πr²
Here, r = 649
Therefore, the area of the circle = π × 649² = 3.14 × 649 × 649 = 1,324,214.46 m².
Problem 4
The area of a square is 421,201 cm². Find the perimeter of the square.
The perimeter of the square is
Explanation
The area of the square = a²
Here, the area is 421,201 cm²
The length of the side is √421,201 = 649
Perimeter of the square = 4a
Here, a = 649
Therefore, the perimeter = 4 × 649 = 2,596.
Problem 5
Find the square of 650.
The square of 650 is 422,500
Explanation
The square of 650 is multiplying 650 by 650.
So, the square = 650 × 650 = 422,500
FAQs on Square of 649
1.What is the square of 649?
2.What is the square root of 649?
3.Is 649 a prime number?
4.What are the first few multiples of 649?
5.What is the square of 648?
Important Glossaries for Square 649.
- Integer: A whole number that can be positive, negative, or zero.
- Exponent: In mathematics, an exponent refers to the number of times a number (the base) is multiplied by itself.
- Perfect Square: A number that is the square of an integer.
- Square Root: The square root of a number is a value that, when multiplied by itself, gives the number.
- Arithmetic: A branch of mathematics dealing with numbers and basic operations such as addition, subtraction, multiplication, and division.
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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.
