Square Root of 1/2

The square root is the inverse of the square of the number. 1/2 is not a perfect square. The square root of 1/2 is expressed in both radical and exponential form. In the radical form, it is expressed as √(1/2), whereas (1/2)^(1/2) in the exponential form. √(1/2) = 0.70710678118, which is an irrational number because it cannot be expressed in the form of p/q, where p and q are integers and q ≠ 0.

The prime factorization method is used for perfect square numbers. However, for non-perfect square numbers like 1/2, methods such as the long-division method and approximation method are used. Let us now learn the following methods:

• Prime factorization method
• Long division method
• Approximation method

The prime factorization method involves expressing a number as the product of prime factors.

Since 1/2 is a fraction and not a whole number, traditional prime factorization is not applicable.

Therefore, calculating 1/2 using prime factorization is not feasible.

The long division method is particularly used for non-perfect square numbers. In this method, we should check the closest perfect square number for the given number. Let us now learn how to find the square root using the long division method, step by step:

Step 1: To begin with, convert 1/2 to a decimal, which is 0.5.

Step 2: Find the closest perfect square numbers around 0.5. The closest are 0.25 (0.5 squared) and 1.

Step 3: Apply the long division method to approximate the square root of 0.5.

Step 4: Continue the division until the desired decimal place accuracy is reached. After following these steps, the square root of 0.5 is approximately 0.70710678118.

Approximation method is another method for finding square roots; it is an easy method to find the square root of a given number. Now let us learn how to find the square root of 1/2 using the approximation method.

Step 1: Convert 1/2 to a decimal, which is 0.5.

Step 2: Identify the closest perfect squares around 0.5, which are 0.25 and 1.

Step 3: Use linear interpolation to approximate the square root, calculating the position of 0.5 between 0.25 and 1.

Using this method, we find that √(0.5) ≈ 0.7071.

• Square root: A square root is the inverse of a square. Example: 4² = 16, and the inverse of the square is the square root, that is, √16 = 4.

• Irrational number: An irrational number is a number that cannot be written in the form of p/q, where q is not equal to zero and p and q are integers.

• Principal square root: A number has both positive and negative square roots; however, it is usually the positive square root, known as the principal square root, that is used in real-world applications.

• Fractions: A fraction represents a part of a whole, expressed as a numerator over a denominator, such as 1/2.

• Decimals: A decimal is a number that uses a decimal point to show a fraction of a base-10 number, such as 0.5.