100 LearnersLast updated on May 26th, 2025
Square Root of 1/144
If a number is multiplied by itself, the result is a square. The inverse operation is finding the square root. The square root is used in various fields such as vehicle design and finance. Here, we will discuss the square root of 1/144.
What is the Square Root of 1/144?
The square root is the inverse of squaring a number. 1/144 is a perfect square. The square root of 1/144 can be expressed in both radical and exponential form. In the radical form, it is expressed as √(1/144), whereas in exponential form, it is (1/144)^(1/2). √(1/144) = 1/12, which is a rational number because it can be expressed in the form of p/q, where p and q are integers and q ≠ 0.
Finding the Square Root of 1/144
The prime factorization method is used for perfect square numbers. Since 1/144 is a perfect square, we can use the prime factorization method to find its square root.
Square Root of 1/144 by Prime Factorization Method
The prime factorization of a number involves expressing it as a product of prime factors. Let's see how 144 is broken down into its prime factors:
Step 1: Finding the prime factors of 144 Breaking it down, we get 2 x 2 x 2 x 2 x 3 x 3: 2^4 x 3^2
Step 2: Now that we have found the prime factors of 144, the next step is to find the square root. Since 144 is a perfect square, we can take the square root of each pair of prime factors. √(1/144) = 1/√144 = 1/(2^2 x 3) = 1/12
Square Root of 1/144 by Long Division Method
The long division method can also be used to find the square root of perfect squares. Let's find the square root of 1/144 using the long division method:
Step 1: Group the digits of 144 from right to left. Since 144 is a perfect square, we can directly find the square root by dividing 144 by 12.
Step 2: Divide 144 by 12 to get the quotient, which is the square root.
Step 3: The result of the division is 12, and since we are finding the square root of 1/144, the answer is 1/12.
Square Root of 1/144 by Approximation Method
Approximation is another method for finding square roots, especially useful for non-perfect squares. However, since 1/144 is a perfect square, we can easily find the square root without approximation.
Step 1: Identify the closest perfect square to 144, which is 144 itself.
Step 2: The square root of 144 is 12, so the square root of 1/144 is 1/12.
Common Mistakes and How to Avoid Them in the Square Root of 1/144
Students may make mistakes while finding the square root, such as forgetting about the negative square root or not simplifying fractions correctly. Let's look at a few common mistakes 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, when dealing with real-world applications, we often take the principal (positive) square root.
For example: √(1/144) = 1/12, but there is also -1/12.
Square Root of 1/144 Examples
Problem 1
Can you help Max find the side length of a square box if its area is given as 1/144 square units?
The side length of the square box is 1/12 units.
Explanation
The side length of a square is the square root of its area. Therefore, the side length is √(1/144) = 1/12 units.
Problem 2
If a square-shaped field measures 1/144 square meters, what will be the perimeter of the field?
The perimeter of the field is 1/3 meters.
Explanation
To find the perimeter, calculate the side length, which is the square root of the area:
√(1/144) = 1/12.
Perimeter = 4 × side length = 4 × (1/12) = 1/3 meters.
Problem 3
Calculate √(1/144) × 6.
0.5
Explanation
First, find the square root of 1/144, which is 1/12. Then multiply 1/12 by 6: 1/12 × 6 = 6/12 = 0.5
Problem 4
What will be the square root of (1/144 + 1/144)?
The square root is 1/6.
Explanation
First, find the sum of (1/144 + 1/144) = 2/144 = 1/72. Then find the square root: √(1/72) = 1/√72 = 1/(√(36 × 2)) = 1/(6√2). Simplifying further, we get approximately 1/6.
Problem 5
Find the perimeter of a rectangle if its length 'l' is 1/12 units and the width 'w' is 1 unit.
The perimeter of the rectangle is 26/12 units or 2.1667 units.
Explanation
Perimeter of the rectangle = 2 × (length + width) Perimeter = 2 × (1/12 + 1) = 2 × (1/12 + 12/12) = 2 × (13/12) = 26/12 units.
FAQ on Square Root of 1/144
1.What is √(1/144) in its simplest form?
2.Mention the factors of 144.
3.Calculate the square of 1/12.
4.Is 144 a perfect square?
5.Is 1/144 a rational number?
Important Glossaries for the Square Root of 1/144
- Square root: A square root is the inverse operation of squaring a number. For example, the square root of 16 is 4 because 4 × 4 = 16.
- Rational number: A rational number is a number that can be expressed as a fraction p/q, where p and q are integers and q is not zero.
- Perfect square: A perfect square is an integer that is the square of an integer. For example, 144 is a perfect square because it is 12 × 12.
- Fraction: A fraction represents a part of a whole or, more generally, any number of equal parts. It is expressed as p/q, where p and q are integers, and q is not zero.
- Perimeter: The perimeter is the total length around a two-dimensional shape. For a rectangle, it is calculated as 2 × (length + width).
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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
: He loves to play the quiz with kids through algebra to make kids love it.
