132 LearnersLast updated on May 26th, 2025
Square Root of 4/5
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 4/5.
What is the Square Root of 4/5?
The square root is the inverse of squaring a number. 4/5 is not a perfect square. The square root of 4/5 can be expressed in both radical and exponential form. In radical form, it is expressed as √(4/5), whereas in exponential form, it is expressed as (4/5)^(1/2). √(4/5) = √4/√5 = 2/√5. This is an irrational number because it cannot be expressed as a simple fraction p/q, where p and q are integers and q ≠ 0.
Finding the Square Root of 4/5
The prime factorization method is typically used for perfect square numbers. For non-perfect square numbers like 4/5, we use simplification and rationalization. Let us learn the following methods:
Simplification and rationalization Decimal approximation
Square Root of 4/5 by Simplification and Rationalization
To find the square root of a fraction, we take the square root of the numerator and the denominator separately.
Step 1: Find the square roots of the numerator and the denominator separately. √4 = 2 and √5 is left as is because it is an irrational number.
Step 2: Express the square root of the fraction. √(4/5) = √4/√5 = 2/√5.
Step 3: Rationalize the denominator. Multiply both the numerator and the denominator by √5 to remove the radical from the denominator: (2/√5) × (√5/√5) = 2√5/5.
Square Root of 4/5 by Decimal Approximation
Decimal approximation is another method to find the square root of a given number.
Step 1: Find the decimal form of 4/5, which is 0.8.
Step 2: Use a calculator to approximate √0.8. √0.8 ≈ 0.8944.
Common Mistakes and How to Avoid Them in the Square Root of 4/5
Students often make mistakes when calculating square roots, such as forgetting about the negative square root, skipping steps in rationalization, or misapplying decimal approximations. Here, we will explore some common mistakes in detail.
Mistake 1
Forgetting about the negative square root
It is important to remember that a number has both positive and negative square roots. However, we typically consider only the positive square root in practical applications.
For example, √(4/5) = ±2/√5, but we usually take the positive root.
Mistake 2
Incorrect rationalization of the denominator
Students sometimes incorrectly multiply the numerator and denominator by the same radical, failing to simplify correctly. Ensure that the multiplication of the rationalizing factor is correctly applied to both the numerator and denominator.
Mistake 3
Mistaking square roots for cube roots
Square root and cube root symbols are often confused. Ensure students understand the difference: √(4/5) is a square root, not a cube root, which would be denoted as ∛(4/5).
Mistake 4
Using an incorrect formula for decimal approximation
Decimal approximations must be calculated accurately using a calculator or appropriate method. Missteps in typing or calculation can lead to incorrect results.
Mistake 5
Misinterpretation of the resulting fraction
When the square root results in a fraction, ensure students understand the correct interpretation and simplification, especially when the denominator needs rationalization.
Square Root of 4/5 Examples
Problem 1
A rectangle has an area of 4/5 square units. What is the length of a side if it is a square?
The side length is approximately 0.8944 units.
Explanation
Since the area of the square is 4/5, which is 0.8, the side length is the square root of the area. √0.8 ≈ 0.8944.
Therefore, the side length is approximately 0.8944 units.
Problem 2
If you multiply the square root of 4/5 by 5, what is the result?
The result is approximately 4.472.
Explanation
First, find the square root of 4/5, which is approximately 0.8944.
Multiply this by 5: 0.8944 × 5 = 4.472.
Problem 3
What is the square root of (4/5)²?
The square root is 4/5.
Explanation
The square root of a square returns the original number: √((4/5)²) = 4/5.
FAQ on Square Root of 4/5
1.What is √(4/5) in its simplest form?
2.Is 4/5 a rational number?
3.What is the decimal value of √(4/5)?
4.Can √(4/5) be expressed as a whole number?
5.How do you rationalize the denominator of 2/√5?
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 4/5?
8.How do technology and digital tools in Vietnam support learning Algebra and Square Root of 4/5?
9.Does learning Algebra support future career opportunities for students in Vietnam?
Important Glossaries for the Square Root of 4/5
- Square root: The square root of a number is a value that, when multiplied by itself, gives the original number. Example: √9 = 3 because 3 × 3 = 9.
- Irrational number: An irrational number cannot be expressed as a simple fraction. It is non-repeating and non-terminating in decimal form.
- Rationalization: The process of eliminating a radical from the denominator of a fraction by multiplying the numerator and the denominator by a suitable radical.
- Decimal approximation: The process of finding a decimal number close to the value of an irrational number.
- Fraction: A numerical quantity that is not a whole number, represented by two integers, a numerator and a denominator.
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About BrightChamps in Vietnam
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.
