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 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.
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:
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.
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.
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.
Students may make mistakes while finding the square root, like forgetting about the negative square root or misapplying methods. Here are some common errors:
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.
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.
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
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.
Calculate √(12/3) x 5.
10
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.
What will be the square root of (12/3 + 6)?
The square root is √10.
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.
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.
Perimeter of the rectangle = 2 × (length + width).
Perimeter = 2 × (√4 + 3) = 2 × (2 + 3) = 2 × 5 = 10 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.