Last updated on May 26th, 2025
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.
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.
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:
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.
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.
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.
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.
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.
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.
The side length of a square is the square root of its area.
Thus, the side length is √(8/3) ≈ 1.633 meters.
Calculate √(8/3) x 5.
Approximately 8.165.
First, find the square root of 8/3, which is approximately 1.633, then multiply by 5: 1.633 x 5 ≈ 8.165.
What will be the square root of (8/3 + 1)?
Approximately 1.915.
First, compute 8/3 + 1 = 11/3.
Then, find √(11/3) ≈ 1.915.
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.
: He loves to play the quiz with kids through algebra to make kids love it.