103 LearnersLast updated on May 26th, 2025
Square Root of 6400
If a number is multiplied by the same number, the result is a square. The inverse of the square is a square root. The square root is used in the field of vehicle design, finance, etc. Here, we will discuss the square root of 6400.
What is the Square Root of 6400?
The square root is the inverse of the square of the number. 6400 is a perfect square. The square root of 6400 is expressed in both radical and exponential form. In the radical form, it is expressed as √6400, whereas (6400)^(1/2) in the exponential form. √6400 = 80, which is a rational number because it can be expressed in the form of p/q, where p and q are integers and q ≠ 0.
Finding the Square Root of 6400
The prime factorization method is used for perfect square numbers, and the long-division method is used for both perfect and non-perfect square numbers. Let us now learn the following methods:
- Prime factorization method
- Long division method
Square Root of 6400 by Prime Factorization Method
The product of prime factors is the prime factorization of a number. Now let us look at how 6400 is broken down into its prime factors.
Step 1: Finding the prime factors of 6400 Breaking it down, we get 2 x 2 x 2 x 2 x 2 x 2 x 5 x 5: 2^6 x 5^2
Step 2: Now we found out the prime factors of 6400. The second step is to make pairs of those prime factors. Since 6400 is a perfect square, we can group these factors into pairs: (2^3 x 5)^2.
Step 3: Taking the square root of both sides gives √6400 = (2^3 x 5) = 8 x 5 = 40.
Square Root of 6400 by Long Division Method
The long division method is particularly used for both perfect and non-perfect square numbers. Let us now learn how to find the square root using the long division method, step by step.
Step 1: To begin with, we need to group the numbers from right to left. In the case of 6400, we need to group it as 64 and 00.
Step 2: Now we need to find n whose square is less than or equal to 64. We can say n as ‘8’ because 8 x 8 = 64, which is equal to 64. Now the quotient is 8. Step 3: Since 6400 ends in double zeros, the square root will also have a zero, making it 80.
So the square root of √6400 is 80.
Square Root of 6400 by Approximation Method
The approximation method is another method for finding the square roots, it is an easy method to find the square root of a given number. Now let us learn how to find the square root of 6400 using the approximation method.
Step 1: Now we have to find the closest perfect square of √6400. The perfect square closest to 6400 is 6400 itself. √6400 is exactly 80. Thus, the square root of 6400 is 80.
Common Mistakes and How to Avoid Them in the Square Root of 6400
Students do make mistakes while finding the square root, like forgetting about the negative square root, skipping long division methods, etc. Now let us look at a few of those mistakes that students tend to make in detail.
Mistake 1
Forgetting about the negative square root
It is important to make students aware that a number does have both positive and negative square roots. However, we will be taking only the positive square root, as it is the required one.
For example: √6400 = 80, there is also -80 which should not be forgotten.
Square root of 6400 Examples
Problem 1
Can you help Max find the area of a square box if its side length is given as √6400?
The area of the square is 6400 square units.
Explanation
The area of the square = side^2.
The side length is given as √6400.
Area of the square = side^2 = √6400 x √6400 = 80 x 80 = 6400.
Therefore, the area of the square box is 6400 square units.
Problem 2
A square-shaped building measuring 6400 square feet is built; if each of the sides is √6400, what will be the square feet of half of the building?
3200 square feet.
Explanation
We can just divide the given area by 2 as the building is square-shaped.
Dividing 6400 by 2 = we get 3200.
So half of the building measures 3200 square feet.
Problem 3
Calculate √6400 x 5.
400
Explanation
The first step is to find the square root of 6400, which is 80.
The second step is to multiply 80 by 5.
So 80 x 5 = 400.
Problem 4
What will be the square root of (3600 + 2800)?
The square root is 100.
Explanation
To find the square root, we need to find the sum of (3600 + 2800). 3600 + 2800 = 6400, and then √6400 = 80.
Therefore, the square root of (3600 + 2800) is ±80.
Problem 5
Find the perimeter of a rectangle if its length ‘l’ is √6400 units and the width ‘w’ is 40 units.
The perimeter of the rectangle is 240 units.
Explanation
Perimeter of the rectangle = 2 × (length + width)
Perimeter = 2 × (√6400 + 40) = 2 × (80 + 40) = 2 × 120 = 240 units.
FAQ on Square Root of 6400
1.What is √6400 in its simplest form?
2.Mention the factors of 6400.
3.Calculate the square of 80.
4.Is 6400 a prime number?
5.6400 is divisible by?
6.How does learning Algebra help students in Vietnam make better decisions in daily life?
7.How can cultural or local activities in Vietnam support learning Algebra topics such as Square Root of 6400?
8.How do technology and digital tools in Vietnam support learning Algebra and Square Root of 6400?
9.Does learning Algebra support future career opportunities for students in Vietnam?
Important Glossaries for the Square Root of 6400
- Square Root: A square root is the inverse of a square. Example: 8^2 = 64 and the inverse of the square is the square root, that is √64 = 8.
- Rational Number: A rational number is a number that can be written in the form of p/q, where q is not equal to zero and p and q are integers.
- Perfect Square: A number is a perfect square if it is the square of an integer. For example, 6400 is a perfect square because it is 80^2.
- Factorization: Factorization is the process of breaking down a number into its prime factors. For example, the factorization of 6400 is 2^6 x 5^2.
- Long Division Method: A method used to find the square root of a number involving division in a step-by-step manner.
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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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