126 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.
Mistake 2
Not simplifying fractions correctly
When finding the square root of a fraction, it's crucial to simplify it correctly.
For example, √(1/144) should be simplified to 1/12, not left unsimplified.
Mistake 3
Confusing square roots with cube roots
Students may confuse square roots with cube roots. It's important to differentiate between the two.
For example, √(1/144) is not the same as ∛(1/144).
Mistake 4
Not recognizing perfect squares
Failing to recognize that 144 is a perfect square can lead to incorrect calculations. Recognizing perfect squares can simplify the process of finding square roots.
Mistake 5
Errors in division
When using the long division method, students might make errors in division, leading to incorrect results. It is important to practice division skills to avoid such mistakes.
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.
