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 the field of vehicle design, finance, etc. Here, we will discuss the square root of 1/3.
The square root is the inverse of the square of the number. 1/3 is not a perfect square. The square root of 1/3 is expressed in both radical and exponential form. In the radical form, it is expressed as √(1/3), whereas (1/3)^(1/2) in the exponential form. The square root of 1/3 is approximately 0.57735, 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, the prime factorization method is not used for non-perfect square numbers where 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. In this method, we should check the closest perfect square number for the given number. Let us now learn how to find the square root of 1/3 using the long division method, step by step:
Step 1: To begin with, we consider 1/3, which is 0.333...
Step 2: Estimate a number close to 0.333... whose square is less than or equal to this number. We start with 0.5 since 0.5^2 = 0.25.
Step 3: Improve the approximation by using the long division method to find a more accurate value.
Step 4: Continue the long division steps to find more precise decimal places.
The square root of 1/3 is approximately 0.57735.
The approximation method is another method for finding square roots; 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 1/3 using the approximation method.
Step 1: Now we have to find the closest perfect squares around 1/3. The closest perfect squares to 1/3 are 0.25 (which is 0.5^2) and 0.5625 (which is 0.75^2). The square root of 1/3 falls somewhere between 0.5 and 0.75.
Step 2: Apply the formula for linear approximation between these two points. Using the approximation method, we conclude the square root of 1/3 is approximately 0.57735.
Students make mistakes while finding square roots, such as forgetting about the negative square root or skipping steps in methods. Now let us look at a few of those mistakes that students tend to make in detail.
Can you help Max find the area of a square box if its side length is given as √(1/6)?
The area of the square is approximately 0.1667 square units.
The area of the square = side^2.
The side length is given as √(1/6).
Area of the square = (√(1/6))^2 = 1/6 ≈ 0.1667.
Therefore, the area of the square box is approximately 0.1667 square units.
A square-shaped building measuring 1/3 square feet is built; if each of the sides is √(1/3), what will be the square feet of half of the building?
0.1667 square feet
We can just divide the given area by 2 as the building is square-shaped.
Dividing 1/3 by 2 = 1/6 ≈ 0.1667.
So half of the building measures approximately 0.1667 square feet.
Calculate √(1/3) × 5.
Approximately 2.88675
The first step is to find the square root of 1/3, which is approximately 0.57735.
The second step is to multiply 0.57735 by 5.
So, 0.57735 × 5 ≈ 2.88675.
What will be the square root of (1/6 + 1/12)?
Approximately 0.6455
To find the square root, first find (1/6 + 1/12).
1/6 + 1/12 = 2/12 + 1/12 = 3/12 = 1/4.
The square root of 1/4 is 1/2 = 0.5.
Therefore, the square root of (1/6 + 1/12) is 0.5.
Find the perimeter of the rectangle if its length ‘l’ is √(1/3) units and the width ‘w’ is 1 unit.
Approximately 3.1547 units.
Perimeter of the rectangle = 2 × (length + width).
Perimeter = 2 × (√(1/3) + 1) = 2 × (0.57735 + 1) ≈ 2 × 1.57735 ≈ 3.1547 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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