134 LearnersLast updated on May 26th, 2025
Square Root of 3/8
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.
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.
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
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.
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.
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.
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
Forgetting to Rationalize the Denominator
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.
Mistake 2
Incorrect Conversion of Fractions to Decimals
Students might incorrectly convert the fraction to decimal form. It is crucial to remember that 3 divided by 8 is 0.375, not any other number.
Mistake 3
Not Simplifying Fractions Properly
Simplifying fractions inside a square root is important to avoid mistakes.
For example, √(12/16) reduces to √(3/4), not directly to other forms.
Mistake 4
Confusing Cube Root with Square Root
Students should understand the difference between cube root and square root.
For example, √(3/8) is different from ∛(3/8).
Mistake 5
Errors in Long Division
Finding the square root using the long division method involves many steps. Due to this, students might skip a step accidentally, leading to incorrect results.
Square Root of 3/8 Examples
Problem 1
Can you help Max find the area of a square box if its side length is given as √(3/8)?
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.
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?
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.
Problem 3
Calculate √(3/8) x 5.
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.
Problem 4
What will be the square root of (3+5/8)?
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.
Problem 5
Find the perimeter of the rectangle if its length ‘l’ is √(3/8) units and the width ‘w’ is 4 units.
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.
FAQ on Square Root of 3/8
1.What is √(3/8) in its simplest form?
2.Calculate the square of 3/8.
3.Is 3/8 a perfect square?
4.How do you convert 3/8 into decimal form?
5.What is the reciprocal of 3/8?
6.How does learning Algebra help students in Australia make better decisions in daily life?
7.How can cultural or local activities in Australia support learning Algebra topics such as Square Root of 3/8?
8.How do technology and digital tools in Australia support learning Algebra and Square Root of 3/8?
9.Does learning Algebra support future career opportunities for students in Australia?
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.
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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.
Fun Fact
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