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Last updated on May 26th, 2025

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Square Root of 3/8

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If a number is multiplied by itself, the result is a square. The inverse of the square is a square root. The square root is used in fields such as vehicle design, finance, etc. Here, we will discuss the square root of 3/8.

Square Root of 3/8 for Indonesian Students
Professor Greenline from BrightChamps

What is the Square Root of 3/8?

The square root is the inverse of the square of a number. The fraction 3/8 is not a perfect square. The square root of 3/8 is expressed in both radical and exponential forms. In the radical form, it is expressed as √(3/8), whereas (3/8)^(1/2) in the exponential form. √(3/8) = √3/√8 = √3/(2√2) which simplifies to √6/4. 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.

Professor Greenline from BrightChamps

Finding the Square Root of 3/8

Various methods can be used to find the square root of fractions or non-perfect square numbers, such as the long-division method and approximation method. Let us now learn the following methods:

 

  • Simplifying the radical
  • Long division method
  • Approximation method
Professor Greenline from BrightChamps

Square Root of 3/8 by Simplifying the Radical

To simplify the square root of a fraction, we take the square root of the numerator and the square root of the denominator separately.

 

Step 1: Find the square root of the numerator and the denominator separately: √3 and √8.

 

Step 2: Simplify the expression: √(3/8) = √3/√8.

 

Step 3: Multiply the numerator and denominator by √2 to rationalize the denominator: √3/√8 = √3/(2√2) = √6/4.

Professor Greenline from BrightChamps

Square Root of 3/8 by Long Division Method

The long division method is particularly useful for approximating square roots of non-perfect squares. In this method, we should check the closest perfect square number for the given fraction.

 

Step 1: Convert 3/8 into decimal form: 3 divided by 8 is 0.375.

 

Step 2: Use the long division method to find the square root of 0.375 (as we would for any decimal number).

 

Step 3: Continue the division process until you reach the desired precision.

 

The approximate square root of 0.375 is 0.612372.

Professor Greenline from BrightChamps

Square Root of 3/8 by Approximation Method

The approximation method is another method for finding square roots, and it is an easy method to find the square root of a given number. Now let us learn how to find the square root of 3/8 using the approximation method.

 

Step 1: Convert 3/8 into decimal form: 0.375.

 

Step 2: Find two perfect squares that 0.375 lies between. For example, 0.25 (0.5^2) and 0.36 (0.6^2).

 

Step 3: Use interpolation to approximate the square root: 0.375 is closer to 0.36, so the square root is closer to 0.6.

 

Step 4: Using interpolation, approximate √0.375 as approximately 0.612.

Max Pointing Out Common Math Mistakes

Common Mistakes and How to Avoid Them in the Square Root of 3/8

Students often make mistakes while finding the square root, such as forgetting to rationalize the denominator or incorrectly converting fractions to decimals. Let us look at a few of these mistakes in detail.

Mistake 1

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Forgetting to Rationalize the Denominator

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Rationalizing the denominator is an important step in simplifying square roots of fractions.

For example, when finding √(3/8), students may leave it as √3/√8. However, the correct form is √6/4 after rationalization.

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Square Root of 3/8 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 √(3/8)?

Ray, the Boy Character from BrightChamps Saying "Let’s Begin"

The area of the square is 0.140625 square units.

Explanation

The area of the square = side^2.

The side length is given as √(3/8).

Area of the square = (√(3/8))^2

= 3/8

= 0.375

Therefore, the area of the square box is 0.375 square units.

Max from BrightChamps Praising Clear Math Explanations
Max, the Girl Character from BrightChamps

Problem 2

A square-shaped building measuring 3/8 square feet is built; if each of the sides is √(3/8), what will be the square feet of half of the building?

Ray, the Boy Character from BrightChamps Saying "Let’s Begin"

0.1875 square feet

Explanation

We can just divide the given area by 2 as the building is square-shaped.

Dividing 3/8 by 2 = we get 3/16 = 0.1875.

So half of the building measures 0.1875 square feet.

Max from BrightChamps Praising Clear Math Explanations
Max, the Girl Character from BrightChamps

Problem 3

Calculate √(3/8) x 5.

Ray, the Boy Character from BrightChamps Saying "Let’s Begin"

3.06186

Explanation

First, find the square root of 3/8, which is approximately 0.612372, then multiply it by 5.

So, 0.612372 x 5 = 3.06186.

Max from BrightChamps Praising Clear Math Explanations
Max, the Girl Character from BrightChamps

Problem 4

What will be the square root of (3+5/8)?

Ray, the Boy Character from BrightChamps Saying "Let’s Begin"

0.935414

Explanation

First, find the sum of (3 + 5/8). 3 + 5/8 = 3.625, then find the square root of 3.625, which is approximately 1.903.

Therefore, the square root of (3+5/8) is approximately 1.903.

Max from BrightChamps Praising Clear Math Explanations
Max, the Girl Character from BrightChamps

Problem 5

Find the perimeter of the rectangle if its length ‘l’ is √(3/8) units and the width ‘w’ is 4 units.

Ray, the Boy Character from BrightChamps Saying "Let’s Begin"

We find the perimeter of the rectangle as 9.224744 units.

Explanation

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

Perimeter = 2 × (√(3/8) + 4)

= 2 × (0.612372 + 4)

= 2 × 4.612372

= 9.224744 units.

Max from BrightChamps Praising Clear Math Explanations
Ray Thinking Deeply About Math Problems

FAQ on Square Root of 3/8

1.What is √(3/8) in its simplest form?

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2.Calculate the square of 3/8.

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3.Is 3/8 a perfect square?

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4.How do you convert 3/8 into decimal form?

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5.What is the reciprocal of 3/8?

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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 3/8?

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

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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 3/8

  • Square root: A square root is the inverse of a square. For example, 4^2 = 16 and the inverse of the square is the square root, so √16 = 4.
     
  • Irrational number: An irrational number is a number that cannot be written in the form of p/q, where q is not equal to zero and p and q are integers.
     
  • Decimal: If a number has a whole number and a fraction in a single number, it is called a decimal. For example, 7.86, 8.65, and 9.42 are decimals.
     
  • Rationalize: Rationalizing is the process of eliminating the square root or cube root from the denominator of a fraction.
     
  • Fraction: A fraction represents a part of a whole and is expressed as a ratio of two numbers, such as 3/8.
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 3/8 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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