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Last updated on May 26th, 2025

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Square Root of 4/3

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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.

Square Root of 4/3 for Indonesian Students
Professor Greenline from BrightChamps

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.

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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
Professor Greenline from BrightChamps

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.

Professor Greenline from BrightChamps

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.

Professor Greenline from BrightChamps

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.

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Square Root of 4/3 Examples

Ray, the Character from BrightChamps Explaining Math Concepts
Max, the Girl Character from BrightChamps

Problem 1

Can you help Max find the length of the diagonal of a square if its side length is √(4/3)?

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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.

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Max, the Girl Character from BrightChamps

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?

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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.

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Max, the Girl Character from BrightChamps

Problem 3

Calculate √(4/3) × 6.

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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.

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Max, the Girl Character from BrightChamps

Problem 4

What will be the square root of (4/3 + 8/3)?

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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.

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Max, the Girl Character from BrightChamps

Problem 5

Find the perimeter of a rectangle if its length ‘l’ is √(4/3) units and the width ‘w’ is 2 units.

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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.

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FAQ on Square Root of 4/3

1.What is √(4/3) in its simplest form?

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2.What is the decimal approximation of √(4/3)?

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3.Is 4/3 a perfect square?

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4.Is √(4/3) rational or irrational?

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5.What is the square of √(4/3)?

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6.How does learning Algebra help students in Indonesia make better decisions in daily life?

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7.How can cultural or local activities in Indonesia support learning Algebra topics such as Square Root of 4/3?

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8.How do technology and digital tools in Indonesia support learning Algebra and Square Root of 4/3?

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9.Does learning Algebra support future career opportunities for students in Indonesia?

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Professor Greenline from BrightChamps

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.
Professor Greenline from BrightChamps

About BrightChamps in Indonesia

At BrightChamps, we believe algebra is more than symbols—it’s a doorway to endless possibilities! We aim to help children throughout Indonesia master key math skills, focusing today on the Square Root of 4/3 with a special emphasis on square roots—in a way that’s fun, lively, and easy to understand. Whether your child is measuring the speed of a roller coaster at Dunia Fantasi, tracking scores in badminton matches, or managing their allowance for the latest gadgets, mastering algebra builds the confidence they need for everyday problems. Our hands-on lessons make learning simple and enjoyable. Because children in Indonesia learn differently, we tailor our approach to fit each learner’s needs. From Jakarta’s bustling streets to Bali’s scenic beaches, BrightChamps brings math to life, making it relevant and exciting across Indonesia. Let’s make square roots a fun part of every child’s math journey!
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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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Max, the Girl Character from BrightChamps

Fun Fact

: He loves to play the quiz with kids through algebra to make kids love it.

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