Last updated on August 5th, 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.
Struggling with Math?
Get 1:1 Coaching to Boost Grades Fast !
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.
Level Up with a Math Certification!
2X Faster Learning (Grades 1-12)
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.
Turn your child into a math star!
#1 Math Hack Schools Won't Teach!
Struggling with Math?
Get 1:1 Coaching to Boost Grades Fast !
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.