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:

• Prime factorization method
• Long division method
• Approximation 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.

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:

• 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.