Last updated on May 26th, 2025
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.
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.
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
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.
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.
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.
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.
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.
If you multiply the square root of 4/5 by 5, what is the result?
The result is approximately 4.472.
First, find the square root of 4/5, which is approximately 0.8944.
Multiply this by 5: 0.8944 × 5 = 4.472.
What is the square root of (4/5)²?
The square root is 4/5.
The square root of a square returns the original number: √((4/5)²) = 4/5.
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.
: He loves to play the quiz with kids through algebra to make kids love it.