BrightChamps Logo
Login
Creative Math Ideas Image
Live Math Learners Count Icon103 Learners

Last updated on May 26th, 2025

Math Whiteboard Illustration

Square Root of 3/8

Professor Greenline Explaining Math Concepts

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 Singaporean 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

Red Cross Icon Indicating Mistakes to Avoid in This Math Topic

Forgetting to Rationalize the Denominator

Green Checkmark Icon Indicating Correct Solutions in This Math Topic

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.

Max from BrightChamps Saying "Hey"

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?

Math FAQ Answers Dropdown Arrow

2.Calculate the square of 3/8.

Math FAQ Answers Dropdown Arrow

3.Is 3/8 a perfect square?

Math FAQ Answers Dropdown Arrow

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

Math FAQ Answers Dropdown Arrow

5.What is the reciprocal of 3/8?

Math FAQ Answers Dropdown Arrow

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

Math FAQ Answers Dropdown Arrow

7.How can cultural or local activities in Singapore support learning Algebra topics such as Square Root of 3/8?

Math FAQ Answers Dropdown Arrow

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

Math FAQ Answers Dropdown Arrow

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

Math FAQ Answers Dropdown Arrow
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 Singapore

At BrightChamps, we see algebra as more than just symbols—it opens up a world of opportunities! We’re committed to helping children across Singapore develop essential math skills, focusing today on the Square Root of 3/8 with a special focus on understanding square roots—in an engaging, lively, and simple way. Whether your child is figuring out how fast a roller coaster speeds at Universal Studios Singapore, keeping track of football match scores, or managing their allowance for the newest gadgets, mastering algebra boosts their confidence in daily life. Our interactive lessons make learning fun and accessible. Because kids in Singapore learn in various ways, we customize our teaching to fit each child’s style. From bustling city streets to scenic gardens, BrightChamps makes math come alive throughout Singapore. Let’s make square roots an exciting part of every child’s math adventure!
Math Teacher Background Image
Math Teacher Image

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.

Math Teacher Fun Facts Image
Max, the Girl Character from BrightChamps

Fun Fact

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

INDONESIA - Axa Tower 45th floor, JL prof. Dr Satrio Kav. 18, Kel. Karet Kuningan, Kec. Setiabudi, Kota Adm. Jakarta Selatan, Prov. DKI Jakarta
INDIA - H.No. 8-2-699/1, SyNo. 346, Rd No. 12, Banjara Hills, Hyderabad, Telangana - 500034
SINGAPORE - 60 Paya Lebar Road #05-16, Paya Lebar Square, Singapore (409051)
USA - 251, Little Falls Drive, Wilmington, Delaware 19808
VIETNAM (Office 1) - Hung Vuong Building, 670 Ba Thang Hai, ward 14, district 10, Ho Chi Minh City
VIETNAM (Office 2) - 143 Nguyễn Thị Thập, Khu đô thị Him Lam, Quận 7, Thành phố Hồ Chí Minh 700000, Vietnam
Dubai - BrightChamps, 8W building 5th Floor, DAFZ, Dubai, United Arab Emirates
UK - Ground floor, Redwood House, Brotherswood Court, Almondsbury Business Park, Bristol, BS32 4QW, United Kingdom