100 LearnersLast updated on May 26th, 2025
Square Root of 12/3
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 12/3.
What is the Square Root of 12/3?
The square root is the inverse of the square of the number. 12/3 simplifies to 4, which is a perfect square. The square root of 12/3 is expressed in both radical and exponential form. In the radical form, it is expressed as √(12/3) = √4, whereas in the exponential form it is (4)^(1/2). √4 = 2, 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 12/3
Since 12/3 simplifies to 4, which is a perfect square, we can use the prime factorization method to find the square root. However, for non-perfect squares, methods such as the long division method and approximation method can be used. Below are the methods:
- Prime factorization method
- Long division method
- Approximation method
Square Root of 12/3 by Prime Factorization Method
The product of prime factors is the prime factorization of a number. Now let us look at how 4 is broken down into its prime factors.
Step 1: Finding the prime factors of 4 Breaking it down, we get 2 x 2.
Step 2: Since 4 is a perfect square, we can group the factors in pairs. Thus, the square root of 4 can be found as √(2 x 2) = 2.
Square Root of 12/3 by Long Division Method
The long division method is typically used for non-perfect square numbers, but it can also apply to perfect squares like 4 to verify results. Here’s how it works for √4:
Step 1: For 4, consider the closest perfect square less than or equal to 4, which is 4 itself.
Step 2: The square of 2 is 4, so 2 is our divisor, and the quotient is also 2.
Step 3: Subtract 4 from 4, resulting in a remainder of zero. Thus, the square root of √4 is 2.
Square Root of 12/3 by Approximation Method
The approximation method is generally used for non-perfect squares, but for educational purposes, it can apply here to verify results.
Step 1: Considering √4, we know it lies between the perfect squares of 1 (1^2) and 4 (2^2).
Step 2: Since 4 is exactly a perfect square, √4 = 2.
Common Mistakes and How to Avoid Them in the Square Root of 12/3
Students may make mistakes while finding the square root, like forgetting about the negative square root or misapplying methods. Here are some common errors:
Square Root of 12/3 Examples
Problem 1
Can you help Max find the area of a square box if its side length is given as √(12/3)?
The area of the square is 4 square units.
Explanation
The area of the square = side^2.
The side length is given as √(12/3) = √4 = 2.
Area of the square = side^2 = 2 x 2 = 4.
Therefore, the area of the square box is 4 square units.
Problem 2
A square-shaped building measuring 12/3 square feet is built; if each of the sides is √(12/3), what will be the square feet of half of the building?
2 square feet
Explanation
The area of the building is 12/3 or 4, as the building is square-shaped.
Dividing 4 by 2 = 2. So half of the building measures 2 square feet.
Problem 3
Calculate √(12/3) x 5.
10
Explanation
The first step is to find the square root of 12/3, which is √4 = 2.
The next step is to multiply 2 by 5.
So 2 x 5 = 10.
Problem 4
What will be the square root of (12/3 + 6)?
The square root is √10.
Explanation
To find the square root, first calculate the sum of (12/3 + 6). 12/3 simplifies to 4, and 4 + 6 = 10.
The square root of 10 is approximately ±3.162.
Problem 5
Find the perimeter of the rectangle if its length ‘l’ is √(12/3) units and the width ‘w’ is 3 units.
We find the perimeter of the rectangle as 10 units.
Explanation
Perimeter of the rectangle = 2 × (length + width).
Perimeter = 2 × (√4 + 3) = 2 × (2 + 3) = 2 × 5 = 10 units.
FAQ on Square Root of 12/3
1.What is √(12/3) in its simplest form?
2.Mention the factors of 12/3.
3.Calculate the square of 12/3.
4.Is 12/3 a prime number?
5.12/3 is divisible by?
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 12/3?
8.How do technology and digital tools in United States support learning Algebra and Square Root of 12/3?
9.Does learning Algebra support future career opportunities for students in United States?
Important Glossaries for the Square Root of 12/3
- 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, which is √16 = 4.
- Rational number: A rational number is a number that can be expressed in the form of p/q, where q is not equal to zero and p and q are integers.
- Perfect square: A perfect square is a number that is the square of an integer. For example, 4, 9, and 16 are perfect squares.
- Prime factorization: Prime factorization is the process of expressing a number as the product of its prime numbers.
- Approximation: Approximation involves finding a value close to the exact answer. For example, the square root of 10 is approximately 3.162.
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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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