Square Root of 0.25

The square root is the inverse of the square of the number. 0.25 is a perfect square. The square root of 0.25 is expressed in both radical and exponential form. In the radical form, it is expressed as √0.25, whereas (0.25)^(1/2) in the exponential form. √0.25 = 0.5, 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.

The prime factorization method is useful for perfect square numbers. The long-division method and approximation method are used for non-perfect square numbers. Let us now learn the following 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 0.25 is broken down into its prime factors.

Step 1: Express 0.25 as a fraction: 0.25 = 1/4.

Step 2: Prime factorize the denominator: 4 = 2 × 2.

Step 3: The square root of 1/4 is √(1/4) = 1/2 = 0.5.

The long division method is particularly used for non-perfect square numbers, but it can also demonstrate the process for perfect squares like 0.25. Let us learn how to find the square root using the long division method, step by step.

Step 1: Set up 0.25 under the long division symbol.

Step 2: Pair the digits from right to left. Here it's just 25 (since we are dealing with decimals, consider it as 25).

Step 3: Find a number whose square is less than or equal to 25. This number is 5 (since 5 × 5 = 25).

Step 4: The quotient is 0.5.

The square root of 0.25 is 0.5.

Approximation method is another way to find square roots, although 0.25 is a perfect square and does not require approximation. However, for demonstration, we approximate.

Step 1: Identify the perfect squares between which 0.25 falls. The perfect squares are 0 (0²) and 1 (1²).

Step 2: Since 0.25 is exactly between 0 and 1, calculate the midpoint, which is 0.5.

Thus, √0.25 = 0.5.

• Square root: A square root is the inverse of a square. Example: 0.5² = 0.25, and the inverse of the square is the square root, that is, √0.25 = 0.5.
   
• Perfect square: A number that has an integer as its square root. Example: 0.25 is a perfect square because its square root is 0.5.
   
• Rational number: A rational number is a number that can be written in the form of p/q, where q is not equal to zero, and p and q are integers.
   
• Decimal: If a number has a whole number and a fraction in a single number, then it is called a decimal. Example: 0.5, 1.25, and 3.75 are decimals.
   
• Principal square root: A number has both positive and negative square roots; however, it is always the positive square root that has more prominence due to its uses in the real world.