138 LearnersLast updated on May 26th, 2025
Square Root of 8/3
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 vehicle design, finance, etc. Here, we will discuss the square root of 8/3.
What is the Square Root of 8/3?
The square root is the inverse of the square of a number. 8/3 is not a perfect square. The square root of 8/3 can be expressed in both radical and exponential form. In radical form, it is expressed as √(8/3), whereas in exponential form, it is (8/3)^(1/2). The square root of 8/3 is approximately 1.63299, which 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 8/3
The prime factorization method is used for perfect square numbers. However, for non-perfect square numbers, methods such as the long-division method and approximation method are used. Let us now learn the following methods:
- Prime factorization method
- Long division method
- Approximation method
Square Root of 8/3 by Long Division Method
The long division method is particularly used for non-perfect square numbers. Let us now learn how to find the square root of 8/3 using the long division method, step by step:
Step 1: Convert the fraction 8/3 to a decimal, which is approximately 2.6667.
Step 2: Group the digits from left to right.
Step 3: Find a number whose square is less than or equal to 2.66. Begin with 1 since 1 x 1 = 1.
Step 4: Subtract 1 from 2.66, bringing down the next pair of digits.
Step 5: Double the current quotient and find a suitable digit to append to it, which when multiplied by itself, gives a product less than or equal to the current dividend. Repeat these steps until the desired accuracy is achieved.
The square root of 8/3 is approximately 1.63299.
Square Root of 8/3 by Approximation Method
The approximation method is another way to find square roots. It is an easy method for estimating the square root of a given number. Here's how to find the square root of 8/3 using the approximation method:
Step 1: Approximate the fraction 8/3 as the decimal 2.6667.
Step 2: Identify the closest perfect squares around 2.6667. The perfect squares 1 (1^2) and 4 (2^2) bracket 2.6667.
Step 3: Use interpolation to estimate between these two values. The linear approximation will give you a result close to 1.63299.
Common Mistakes and How to Avoid Them in Finding the Square Root of 8/3
Students often make mistakes while finding square roots, such as forgetting about the negative square root, skipping long division steps, etc. Let us look at a few of these mistakes in detail.
Mistake 1
Forgetting about the Negative Square Root
It is important to remember that numbers have both positive and negative square roots. However, we usually take only the positive square root, as it is often the required one.
Mistake 2
Not Adding Square Root Symbol in Proper Places
Misusing the square root symbol is a common error. Ensure students simplify the numbers inside the square root correctly before moving to the next step.
Mistake 3
Not Finding the Correct Value of a Non-Perfect Square
Teach students to simplify the numbers inside the square root to avoid mistakes in identifying approximate values.
Mistake 4
Confusing the Square Root Symbol with the Cube Root
Students should be taught the difference between cube root and square root to avoid confusion.
Mistake 5
Making Mistakes in Long Division
The long division method involves many steps, which may lead students to skip steps accidentally, resulting in wrong answers.
Square Root of 8/3 Examples
Problem 1
Can you help Max find the area of a square box if its side length is given as √(8/3)?
The area of the square is approximately 2.667 square units.
Explanation
The area of a square = side^2.
If the side length is √(8/3), then the area = (√(8/3))^2 = 8/3 ≈ 2.667 square units.
Problem 2
A square-shaped garden covers an area of 8/3 square meters. What is the length of each side of the garden?
The length of each side is approximately 1.633 meters.
Explanation
The side length of a square is the square root of its area.
Thus, the side length is √(8/3) ≈ 1.633 meters.
Problem 3
Calculate √(8/3) x 5.
Approximately 8.165.
Explanation
First, find the square root of 8/3, which is approximately 1.633, then multiply by 5: 1.633 x 5 ≈ 8.165.
Problem 4
What will be the square root of (8/3 + 1)?
Approximately 1.915.
Explanation
First, compute 8/3 + 1 = 11/3.
Then, find √(11/3) ≈ 1.915.
FAQ on Square Root of 8/3
1.What is √(8/3) in its simplest form?
2.Is 8/3 a perfect square?
3.How do you calculate the square of 8/3?
4.Is 8/3 greater than 2?
5.What is the decimal approximation of √(8/3)?
6.How does learning Algebra help students in United Kingdom make better decisions in daily life?
7.How can cultural or local activities in United Kingdom support learning Algebra topics such as Square Root of 8/3?
8.How do technology and digital tools in United Kingdom support learning Algebra and Square Root of 8/3?
9.Does learning Algebra support future career opportunities for students in United Kingdom?
Important Glossary for the Square Root of 8/3
- Square root: The square root is the inverse operation of squaring a number. For example, 4^2 = 16, so √16 = 4.
- Irrational number: A number that cannot be expressed as a simple fraction, such as √2 or √(8/3).
- Decimal: A fractional number expressed in base 10, such as 1.63299.
- Radical: An expression that uses the root symbol (√) to denote roots, such as √8.
- Perfect square: A number that is the square of an integer, such as 4 (2^2) or 9 (3^2).
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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
: He loves to play the quiz with kids through algebra to make kids love it.
