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Last updated on May 26th, 2025

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Square Root of 10/3

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If a number is multiplied by itself, the result is a square. The inverse of squaring a number is taking its square root. The square root is used in various fields such as engineering, finance, and physics. Here, we will discuss the square root of 10/3.

Square Root of 10/3 for Bahraini Students
Professor Greenline from BrightChamps

What is the Square Root of 10/3?

The square root is the inverse operation of squaring a number. 10/3 is not a perfect square, so its square root is an irrational number. The square root of 10/3 can be expressed in both radical and exponential form: in radical form as √(10/3), and in exponential form as (10/3)^(1/2). The approximate decimal value is √(10/3) ≈ 1.82574, which is an irrational number because it cannot be expressed as a ratio of two integers.

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Finding the Square Root of 10/3

For non-perfect squares like 10/3, methods such as the long division method and approximation method are used. Let's explore the following methods:

 

  • Long division method
  • Approximation method
Professor Greenline from BrightChamps

Square Root of 10/3 by Long Division Method

The long division method is often used for finding the square root of non-perfect square numbers. It involves a series of steps to approximate the square root:

 

Step 1: Consider the number 10/3 as 3.3333...

 

Step 2: Find two perfect squares between which 3.3333... falls. Here, it lies between 1.772 (√3) and 1.841 (√3.4).

 

Step 3: Apply the long division method to get a more accurate approximation. Step 4: Continue the division until reaching the desired precision.

 

The square root of 10/3 is approximately 1.82574.

Professor Greenline from BrightChamps

Square Root of 10/3 by Approximation Method

The approximation method provides a quick way to estimate the square root:

 

Step 1: Identify perfect squares close to 10/3. The closest perfect square less than 10/3 is 3, and more than 10/3 is 4.

 

Step 2: Use interpolation to approximate: (10/3 - 3) / (4 - 3) = (10/3 - 3).

 

Step 3: Calculate the approximate square root, using the averages: 1.772 + [(10/3 - 3) / (4 - 3)] × (1.841 - 1.772) ≈ 1.82574.

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Common Mistakes and How to Avoid Them in the Square Root of 10/3

Students often make mistakes when finding the square root, such as ignoring the negative square root or misapplying the methods. Let's explore these common mistakes in detail.

Mistake 1

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Forgetting about the Negative Square Root

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It's crucial to remember that a number has both a positive and a negative square root. However, in practical applications, we usually consider the positive square root.

For example, √(10/3) ≈ 1.82574, but there is also -1.82574.

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Square Root of 10/3 Examples

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

Problem 1

Can you help Max find the area of a square box if its side length is given as √(10/3)?

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The area of the square is approximately 3.333 square units.

Explanation

The area of the square = side².

The side length is given as √(10/3).

Area = (√(10/3))² = 10/3 ≈ 3.333.

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Max, the Girl Character from BrightChamps

Problem 2

If a square-shaped parcel covers an area of 10/3 square feet, what is the length of one side of the parcel?

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The length of one side of the parcel is approximately 1.82574 feet.

Explanation

The side length of the square = √(area).

Side length = √(10/3) ≈ 1.82574 feet.

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Max, the Girl Character from BrightChamps

Problem 3

Calculate √(10/3) × 5.

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Approximately 9.1287.

Explanation

First, find √(10/3) ≈ 1.82574. Then, multiply: 1.82574 × 5 ≈ 9.1287.

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Max, the Girl Character from BrightChamps

Problem 4

What is the square root of (10/3) + 3?

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The square root is approximately 2.44949.

Explanation

First, find the sum (10/3) + 3 = 19/3.

Then, find the square root: √(19/3) ≈ 2.44949.

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Max, the Girl Character from BrightChamps

Problem 5

Find the perimeter of a rectangle with length √(10/3) units and width 3 units.

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The perimeter of the rectangle is approximately 9.65148 units.

Explanation

Perimeter of the rectangle = 2 × (length + width).

Perimeter = 2 × (√(10/3) + 3) ≈ 2 × (1.82574 + 3) = 9.65148 units.

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FAQ on Square Root of 10/3

1.What is √(10/3) in its simplest form?

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2.Is 10/3 a rational number?

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3.Calculate the square of √(10/3).

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4.Is √(10/3) a rational number?

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5.What is the approximate decimal value of √(10/3)?

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

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7.How can cultural or local activities in Bahrain support learning Algebra topics such as Square Root of 10/3?

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8.How do technology and digital tools in Bahrain support learning Algebra and Square Root of 10/3?

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

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Professor Greenline from BrightChamps

Important Glossaries for the Square Root of 10/3

  • Square root: The square root of a number is a value that, when multiplied by itself, gives the original number. For example, √4 = 2.

 

  • Irrational number: A number that cannot be expressed as a simple fraction or ratio of two integers, such as √2 or √(10/3).

 

  • Rational number: A number that can be expressed as a fraction or ratio of two integers, like 10/3.

 

  • Decimal approximation: An estimated decimal value of an irrational number or a non-terminating decimal.

 

  • Long division method: A step-by-step method used to find the square root of a number by dividing and averaging.
Professor Greenline from BrightChamps

About BrightChamps in Bahrain

At BrightChamps, we understand algebra as more than symbols—it’s a gateway to countless opportunities! We are dedicated to helping children across Bahrain master essential math skills, focusing today on the Square Root of 10/3 with special attention to square roots—in a fun, lively, and easy-to-follow manner. Whether your child is figuring out the speed of a roller coaster at Bahrain’s Wahooo! Waterpark, following local football scores, or managing their allowance to buy the latest gadgets, mastering algebra builds confidence for daily challenges. Our hands-on lessons make learning simple and enjoyable. Because kids in Bahrain learn differently, we customize our teaching to fit each learner’s style. From Manama’s lively city life to peaceful beaches, BrightChamps brings math to life, making it exciting throughout Bahrain. 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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