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 1/18.
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.
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:
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.
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.
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.
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.
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.
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.
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
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.
Calculate √(1/18) x 5.
1.185
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.
What will be the square root of (1/18 + 1)?
The square root is approximately 1.049.
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.
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.
Perimeter of the rectangle = 2 × (length + width). Perimeter = 2 × (√(1/18) + 2) ≈ 2 × (0.237 + 2) = 2 × 2.237 = 4.474 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.
: He loves to play the quiz with kids through algebra to make kids love it.