103 LearnersLast updated on May 26th, 2025
Square Root of 6.4
If a number is multiplied by itself, the result is a square. The inverse of the square is a square root. The square root is used in fields like vehicle design, finance, etc. Here, we will discuss the square root of 6.4.
What is the Square Root of 6.4?
The square root is the inverse of the square of a number. 6.4 is not a perfect square. The square root of 6.4 is expressed in both radical and exponential form. In the radical form, it is expressed as √6.4, whereas (6.4)^(1/2) in the exponential form. √6.4 ≈ 2.52982, which is an irrational number because it cannot be expressed in the form of p/q, where p and q are integers and q ≠ 0.
Finding the Square Root of 6.4
The prime factorization method is used for perfect square numbers. However, for non-perfect square numbers, methods like the long division method and approximation method are used. Let us learn about the following methods:
- Long division method
- Approximation method
Square Root of 6.4 by Long Division Method
The long division method is particularly used for non-perfect square numbers. In this method, we should check the closest perfect square number for the given number. Let us learn how to find the square root using the long division method, step by step.
Step 1: To begin, we need to group the numbers from right to left. For 6.4, treat it as 64 by considering two decimal places.
Step 2: Find n whose square is less than or equal to 6. We can say n = 2 because 2² = 4, which is less than 6. The quotient is 2, and after subtracting, the remainder is 2.
Step 3: Bring down 40 (from 4.0). Add the old divisor with the same number: 2 + 2 = 4, which will be our new divisor.
Step 4: Find n such that 4n × n ≤ 240. Let n = 5, then 45 × 5 = 225.
Step 5: Subtract 225 from 240, and the remainder is 15.
Step 6: Since the remainder is less than the divisor, add a decimal point and two zeroes to the remainder to make it 1500.
Step 7: Find the new divisor that is 49 because 495 × 5 = 2475.
Step 8: Subtract 2475 from 1500 to get a new remainder. Continue this process until you reach the desired accuracy.
So the square root of √6.4 ≈ 2.53.
Square Root of 6.4 by Approximation Method
The approximation method is an easy method for finding the square roots of non-perfect squares. Here’s how to find the square root of 6.4 using approximation.
Step 1: Identify the closest perfect squares around 6.4.
The smallest perfect square below 6.4 is 4, and the largest perfect square above 6.4 is 9. √6.4 falls between 2 and 3.
Step 2: Apply the formula: (Given number - smallest perfect square) / (Greater perfect square - smallest perfect square). For 6.4, (6.4 - 4) / (9 - 4) = 0.48.
Add this decimal to the smaller perfect square root: 2 + 0.53 = 2.53.
Therefore, the square root of 6.4 is approximately 2.53.
Common Mistakes and How to Avoid Them in the Square Root of 6.4
Students often make mistakes while finding square roots, such as forgetting about the negative square root or skipping methods like long division. Let's review some common errors in detail.
Mistake 1
Forgetting about the negative square root
It is important to make students aware that a number has both positive and negative square roots. However, we typically consider only the positive square root.
For example, √6.4 ≈ 2.53, but there is also -2.53, which should not be forgotten.
Square root of 6.4 Examples
Problem 1
Can you help Max find the area of a square box if its side length is given as √6.4?
The area of the square is approximately 16.04 square units.
Explanation
The area of the square = side².
The side length is given as √6.4.
Area of the square = (√6.4)² ≈ 2.53 × 2.53 ≈ 16.04.
Therefore, the area of the square box is approximately 16.04 square units.
Problem 2
A square-shaped building measuring 6.4 square feet is built; if each of the sides is √6.4, what will be the square feet of half of the building?
3.2 square feet
Explanation
Since the building is square-shaped, dividing the given area by 2 gives the area of half of the building.
Dividing 6.4 by 2 = 3.2.
So half of the building measures 3.2 square feet.
Problem 3
Calculate √6.4 × 5.
Approximately 12.65
Explanation
First, find the square root of 6.4, which is approximately 2.53.
Then multiply 2.53 by 5.
So, 2.53 × 5 ≈ 12.65.
Problem 4
What will be the square root of (4 + 2.4)?
The square root is approximately 2.83.
Explanation
To find the square root, first find the sum of (4 + 2.4). 4 + 2.4 = 6.4, and then √6.4 ≈ 2.53.
Therefore, the square root of (4 + 2.4) is approximately ±2.53.
Problem 5
Find the perimeter of the rectangle if its length ‘l’ is √6.4 units and the width ‘w’ is 3.8 units.
The perimeter of the rectangle is approximately 12.66 units.
Explanation
Perimeter of the rectangle = 2 × (length + width)
Perimeter = 2 × (√6.4 + 3.8) = 2 × (2.53 + 3.8) ≈ 2 × 6.33 ≈ 12.66 units.
FAQ on Square Root of 6.4
1.What is √6.4 in its simplest form?
2.Mention the factors of 6.4.
3.Calculate the square of 6.4.
4.Is 6.4 a prime number?
5.6.4 is divisible by?
6.How does learning Algebra help students in Bahrain make better decisions in daily life?
7.How can cultural or local activities in Bahrain support learning Algebra topics such as Square Root of 6.4?
8.How do technology and digital tools in Bahrain support learning Algebra and Square Root of 6.4?
9.Does learning Algebra support future career opportunities for students in Bahrain?
Important Glossaries for the Square Root of 6.4
- Square root: A square root is the inverse of a square. Example: 4² = 16, and the inverse of the square is the square root; that is, √16 = 4.
- Irrational number: An irrational number is a number that cannot be written in the form of p/q, where q is not equal to zero and p and q are integers.
- Principal square root: A number has both positive and negative square roots, but the positive square root is more commonly used due to its applications in the real world. This is known as the principal square root.
- Decimal: A decimal is a number that has a whole number and a fraction separated by a decimal point, such as 7.86, 8.65, and 9.42.
- Long division method: A method used to find the square root of a number by dividing it into groups and using iterative steps to approximate the square root value.
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About BrightChamps in Bahrain
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.
