Last updated on May 26th, 2025
If a number is multiplied by itself, the result is a square. The inverse of squaring a number is taking its square root. The square root is used in various fields such as engineering, finance, and physics. Here, we will discuss the square root of 10/3.
The square root is the inverse operation of squaring a number. 10/3 is not a perfect square, so its square root is an irrational number. The square root of 10/3 can be expressed in both radical and exponential form: in radical form as √(10/3), and in exponential form as (10/3)^(1/2). The approximate decimal value is √(10/3) ≈ 1.82574, which is an irrational number because it cannot be expressed as a ratio of two integers.
For non-perfect squares like 10/3, methods such as the long division method and approximation method are used. Let's explore the following methods:
The long division method is often used for finding the square root of non-perfect square numbers. It involves a series of steps to approximate the square root:
Step 1: Consider the number 10/3 as 3.3333...
Step 2: Find two perfect squares between which 3.3333... falls. Here, it lies between 1.772 (√3) and 1.841 (√3.4).
Step 3: Apply the long division method to get a more accurate approximation. Step 4: Continue the division until reaching the desired precision.
The square root of 10/3 is approximately 1.82574.
The approximation method provides a quick way to estimate the square root:
Step 1: Identify perfect squares close to 10/3. The closest perfect square less than 10/3 is 3, and more than 10/3 is 4.
Step 2: Use interpolation to approximate: (10/3 - 3) / (4 - 3) = (10/3 - 3).
Step 3: Calculate the approximate square root, using the averages: 1.772 + [(10/3 - 3) / (4 - 3)] × (1.841 - 1.772) ≈ 1.82574.
Students often make mistakes when finding the square root, such as ignoring the negative square root or misapplying the methods. Let's explore these common mistakes in detail.
Can you help Max find the area of a square box if its side length is given as √(10/3)?
The area of the square is approximately 3.333 square units.
The area of the square = side².
The side length is given as √(10/3).
Area = (√(10/3))² = 10/3 ≈ 3.333.
If a square-shaped parcel covers an area of 10/3 square feet, what is the length of one side of the parcel?
The length of one side of the parcel is approximately 1.82574 feet.
The side length of the square = √(area).
Side length = √(10/3) ≈ 1.82574 feet.
Calculate √(10/3) × 5.
Approximately 9.1287.
First, find √(10/3) ≈ 1.82574. Then, multiply: 1.82574 × 5 ≈ 9.1287.
What is the square root of (10/3) + 3?
The square root is approximately 2.44949.
First, find the sum (10/3) + 3 = 19/3.
Then, find the square root: √(19/3) ≈ 2.44949.
Find the perimeter of a rectangle with length √(10/3) units and width 3 units.
The perimeter of the rectangle is approximately 9.65148 units.
Perimeter of the rectangle = 2 × (length + width).
Perimeter = 2 × (√(10/3) + 3) ≈ 2 × (1.82574 + 3) = 9.65148 units.
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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