133 LearnersLast updated on May 26th, 2025
Square Root of 1/3
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 the field of vehicle design, finance, etc. Here, we will discuss the square root of 1/3.
What is 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.
Finding the Square Root of 1/3
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:
- Prime factorization method
- Long division method
- Approximation method
Square Root of 1/3 by Long Division Method
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.
Square Root of 1/3 by Approximation Method
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.
Common Mistakes and How to Avoid Them in the Square Root of 1/3
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.
Mistake 1
Forgetting about the negative square root
It is important to remember that a number has both positive and negative square roots. However, we often refer to the principal (positive) square root.
For example, √(1/3) = 0.57735, but there is also -0.57735 which should not be forgotten.
Mistake 2
Not adding the square root symbol in proper places
Not using the square root properly is another mistake. It is important to simplify the numbers inside the square root before proceeding.
For example, √(a+b) ≠ √a + √b. The correct way is to first add the numbers inside the root and then take the square root.
Mistake 3
Not finding the correct value of a non-perfect square
The first step is to simplify the numbers inside the square root to avoid mistakes while identifying the approximate value.
For example, √(1/3) should be carefully approximated using proper methods.
Mistake 4
Confusing the square root symbol with the cube root
Students need to be taught the difference between cube root and square root constantly as this will help them avoid mistakes.
For example, √(1/3) and ∛(1/3) are different.
Mistake 5
Making mistakes in long division
Finding a square root using the long division method involves many steps. Due to this, many students might accidentally skip a step, resulting in a wrong answer. This may happen in subtracting or elsewhere.
Square Root of 1/3 Examples
Problem 1
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.
Explanation
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.
Problem 2
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
Explanation
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.
Problem 3
Calculate √(1/3) × 5.
Approximately 2.88675
Explanation
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.
Problem 4
What will be the square root of (1/6 + 1/12)?
Approximately 0.6455
Explanation
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.
Problem 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.
Explanation
Perimeter of the rectangle = 2 × (length + width).
Perimeter = 2 × (√(1/3) + 1) = 2 × (0.57735 + 1) ≈ 2 × 1.57735 ≈ 3.1547 units.
FAQ on Square Root of 1/3
1.What is √(1/3) in its simplest form?
2.Is 1/3 an irrational number?
3.Calculate the square of 1/3.
4.Is 1/3 a prime number?
5.What is the reciprocal of 1/3?
6.How does learning Algebra help students in United States make better decisions in daily life?
7.How can cultural or local activities in United States support learning Algebra topics such as Square Root of 1/3?
8.How do technology and digital tools in United States support learning Algebra and Square Root of 1/3?
9.Does learning Algebra support future career opportunities for students in United States?
Important Glossaries for the Square Root of 1/3
- Square root: A square root is the inverse of a square. Example: 2^2 = 4 and the inverse of the square is the square root, √4 = 2.
- Irrational number: An irrational number is a number that cannot be written in the form of p/q, where q is not equal to zero and p and q are integers.
- Rational number: A rational number can be expressed as a fraction where both the numerator and the denominator are integers, and the denominator is not zero.
- Reciprocal: The reciprocal of a number is 1 divided by that number. For example, the reciprocal of 1/3 is 3.
- Approximation: Approximation is the process of finding a value that is close to but not exactly equal to the actual value, often used for irrational numbers.
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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.
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