116 LearnersLast updated on May 26th, 2025
Square Root of 1/18
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 1/18.
What is the Square Root of 1/18?
The square root is the inverse of the square of the number. 1/18 is not a perfect square. The square root of 1/18 is expressed in both radical and exponential form. In the radical form, it is expressed as √(1/18), whereas (1/18)^(1/2) in the exponential form. √(1/18) = 1/√18 = 1/4.24264, 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 1/18
The prime factorization method is used for perfect square numbers. However, the prime factorization method is not used for non-perfect square numbers where the long-division method and approximation method are used. Let us now learn the following methods:
- Prime factorization method
- Division method
- Approximation method
Square Root of 1/18 by Prime Factorization Method
The product of prime factors is the prime factorization of a number. Now let us look at how 18 is broken down into its prime factors:
Step 1: Finding the prime factors of 18 Breaking it down, we get 2 x 3 x 3: 2^1 x 3^2
Step 2: Now we found out the prime factors of 18. The second step is to make pairs of those prime factors. Since 18 is not a perfect square, the digits of the number can’t be grouped in pairs. Therefore, calculating 1/18 using prime factorization is not straightforward.
Square Root of 1/18 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 using the long division method, step by step.
Step 1: To begin with, we need to group the numbers from right to left. In the case of 18, we need to consider it as a whole number first.
Step 2: Now we need to find n whose square is closest to 1. We can say n as ‘1’ because 1 x 1 is less than or equal to 1. Now the quotient is 1 after subtracting 1-1, the remainder is 0.
Step 3: We continue the process for the denominator 18, which gives us a quotient of approximately 4.24264.
Step 4: Since we need the square root of 1/18, we take the reciprocal of the square root of 18, resulting in approximately 0.23570.
Square Root of 1/18 by Approximation Method
The approximation method is another method for finding the 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 1/18 using the approximation method.
Step 1: Now we have to find the closest perfect squares related to √18. The smallest perfect square less than 18 is 16, and the largest perfect square greater than 18 is 25. √18 falls between 4 and 5.
Step 2: Now we need to apply the formula that is (Given number - smallest perfect square) / (Greater perfect square - smallest perfect square). Going by the formula (18 - 16) / (25 - 16) = 2/9 = 0.22 Using the formula, we identify the decimal point of our square root. The next step is adding the value we got initially to the decimal number, which is 4 + 0.22 = 4.22, so the square root of 18 is approximately 4.22. Thus, the square root of 1/18 is approximately 1/4.22 = 0.237.
Common Mistakes and How to Avoid Them in the Square Root of 1/18
Students do make mistakes while finding the square root, like forgetting about the negative square root, skipping long division methods, etc. 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 make students aware that a number does have both positive and negative square roots. However, we will be taking only the positive square root, as it is the required one.
For example: √(1/18) = ±0.237, although we generally use the positive square root.
Mistake 2
Not adding square root symbol in proper places
Not using the square root properly is another mistake that children make. To resolve this, we need to teach children that simplifying the numbers inside the square root is important and then move on to the second step.
For example: √(1/18) = 1/√18 is the correct way.
Mistake 3
Not finding the correct value of a non-perfect square
The first step that needs to be taught to children is to simplify the numbers inside the square root. This is important so that students do not make mistakes while identifying the approximate value.
For example: √18 ≈ 4.24, not 4.
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 keep away from mistakes.
For example: √18 and ∛18 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 skip a step accidentally, which results in a wrong answer at the end of the sum. This may either happen in subtracting or elsewhere.
Square Root of 1/18 Examples
Problem 1
Can you help Max find the area of a square box if its side length is given as √(1/18)?
The area of the square is approximately 0.01389 square units.
Explanation
The area of the square = side^2.
The side length is given as √(1/18).
Area of the square = (√(1/18))^2 = 1/18 ≈ 0.01389.
Therefore, the area of the square box is approximately 0.01389 square units.
Problem 2
A square-shaped building measuring 1/18 square feet is built; if each of the sides is √(1/18), what will be the square feet of half of the building?
0.5/18 square feet
Explanation
We can just divide the given area by 2 as the building is square-shaped.
Dividing 1/18 by 2 = 0.5/18.
So half of the building measures 0.5/18 square feet.
Problem 3
Calculate √(1/18) x 5.
1.185
Explanation
The first step is to find the square root of 1/18, which is approximately 0.237, and the second step is to multiply 0.237 with 5. So 0.237 x 5 ≈ 1.185.
Problem 4
What will be the square root of (1/18 + 1)?
The square root is approximately 1.049.
Explanation
To find the square root, we need to find the sum of (1/18 + 1). 1/18 + 1 = 19/18, and then √(19/18) ≈ 1.049. Therefore, the square root of (1/18 + 1) is approximately ±1.049.
Problem 5
Find the perimeter of the rectangle if its length ‘l’ is √(1/18) units and the width ‘w’ is 2 units.
The perimeter of the rectangle is approximately 4.474 units.
Explanation
Perimeter of the rectangle = 2 × (length + width). Perimeter = 2 × (√(1/18) + 2) ≈ 2 × (0.237 + 2) = 2 × 2.237 = 4.474 units.
FAQ on Square Root of 1/18
1.What is √(1/18) in its simplest form?
2.Mention the factors of 18.
3.Calculate the square of 1/18.
4.Is 18 a prime number?
5.18 is divisible by?
6.How does learning Algebra help students in Singapore make better decisions in daily life?
7.How can cultural or local activities in Singapore support learning Algebra topics such as Square Root of 1/18?
8.How do technology and digital tools in Singapore support learning Algebra and Square Root of 1/18?
9.Does learning Algebra support future career opportunities for students in Singapore?
Important Glossaries for the Square Root of 1/18
- Square root: A square root is the inverse of a square. Example: 4^2 = 16, and the inverse of the square is the square root, that is, √16 = 4.
- 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.
- Reciprocal: The reciprocal of a number is 1 divided by that number. For example, the reciprocal of 2 is 1/2.
- Decimal approximation: A decimal approximation is a way of representing an irrational number with a finite number of decimal places for simplicity.
- Perfect square: A perfect square is a number that is the square of an integer. For example, 16 is a perfect square because it is 4^2.
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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.
Fun Fact
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