104 LearnersLast updated on May 26th, 2025
Square Root of 4/3
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 various fields such as engineering, physics, and statistics. Here, we will discuss the square root of 4/3.
What is the Square Root of 4/3?
The square root is the inverse of the square of the number. 4/3 is not a perfect square. The square root of 4/3 is expressed in both radical and exponential form. In the radical form, it is expressed as √(4/3), whereas (4/3)^(1/2) in the exponential form. √(4/3) = √4/√3 = 2/√3, which can also be expressed as (2√3)/3 when rationalized. This 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 4/3
The prime factorization method is used for perfect square numbers. However, for non-perfect squares like 4/3, the simplifying radical and rationalization method are used. Let us now learn these methods:
- Simplifying radical form
- Rationalization
Square Root of 4/3 by Simplifying Radical Form
To simplify the square root of a fraction, we find the square roots of the numerator and the denominator separately.
Step 1: Identify the square root of the numerator, √4, which is 2.
Step 2: Identify the square root of the denominator, √3, which remains √3 because 3 is not a perfect square.
Step 3: Combine these results as a fraction, resulting in √(4/3) = 2/√3.
Square Root of 4/3 by Rationalization
Rationalization involves eliminating the radical from the denominator.
Step 1: Start with the fraction 2/√3.
Step 2: Multiply both the numerator and the denominator by √3 to eliminate the radical from the denominator.
Step 3: This results in (2√3)/(√3 × √3) = (2√3)/3.
Common Mistakes and How to Avoid Them in the Square Root of 4/3
Students often make mistakes when dealing with square roots, such as forgetting to rationalize or misapplying the properties of radicals. Let's explore some of these errors in detail.
Square Root of 4/3 Examples
Problem 1
Can you help Max find the length of the diagonal of a square if its side length is √(4/3)?
The diagonal of the square is approximately 2.309401 units.
Explanation
The diagonal of a square can be found using the formula √2 × side length.
The side length is √(4/3).
Diagonal = √2 × √(4/3) = √(8/3) = 2√(2/3) ≈ 2.309401.
Problem 2
A rectangular field has an area of 4/3 square meters, with the length being twice the square root of 4/3. What is the width?
The width is approximately 0.57735 meters.
Explanation
Let the width be 'w'.
Area = length × width = (2 × √(4/3)) × w = 4/3.
w = (4/3) / (2 × √(4/3)) = 1/(2√(4/3)) = 1/((4√3)/3) = √3/4. Width ≈ 0.57735 meters.
Problem 3
Calculate √(4/3) × 6.
Approximately 4.6188.
Explanation
First, find the square root of 4/3 which is (2√3)/3.
√(4/3) × 6 = (2√3)/3 × 6 = 4√3 ≈ 4.6188.
Problem 4
What will be the square root of (4/3 + 8/3)?
The square root is approximately 1.8257.
Explanation
First, find the sum of (4/3 + 8/3) = 12/3 = 4.
Then the square root of 4 is ±2.
Therefore, the principal square root is 2.
Problem 5
Find the perimeter of a rectangle if its length ‘l’ is √(4/3) units and the width ‘w’ is 2 units.
The perimeter of the rectangle is approximately 7.3333 units.
Explanation
Perimeter of the rectangle = 2 × (length + width)
Perimeter = 2 × (√(4/3) + 2) = 2 × ((2√3)/3 + 2) ≈ 7.3333 units.
FAQ on Square Root of 4/3
1.What is √(4/3) in its simplest form?
2.What is the decimal approximation of √(4/3)?
3.Is 4/3 a perfect square?
4.Is √(4/3) rational or irrational?
5.What is the square of √(4/3)?
6.How does learning Algebra help students in United Kingdom make better decisions in daily life?
7.How can cultural or local activities in United Kingdom support learning Algebra topics such as Square Root of 4/3?
8.How do technology and digital tools in United Kingdom support learning Algebra and Square Root of 4/3?
9.Does learning Algebra support future career opportunities for students in United Kingdom?
Important Glossaries for the Square Root of 4/3
- Square root: A square root is the inverse of a square. Example: 4 = 2², and the inverse of the square is the square root, √4 = 2.
- Irrational number: An irrational number cannot be expressed as a ratio of two integers. For example, √3 is irrational.
- Rationalization: The process of eliminating a radical from the denominator of a fraction.
- Radical: An expression that uses the root symbol, such as √3, which denotes the square root of 3.
- Fraction: A numerical quantity that is not a whole number, represented by two numbers separated by a slash, like 4/3.
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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.
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