Square Root of 0.0025

The square root is the inverse of the square of the number. 0.0025 is a perfect square. The square root of 0.0025 is expressed in both radical and exponential form. In radical form, it is expressed as √0.0025, whereas (0.0025)^(1/2) in exponential form. √0.0025 = 0.05, 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 used for perfect square numbers. In the case of non-perfect squares, other methods like 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 product of prime factors is the prime factorization of a number. Now let us look at how 0.0025 is broken down into its prime factors:

Step 1: Convert 0.0025 into a fraction, which is 25/10000.

Step 2: Find the prime factors of 25 and 10000: 25 = 5 × 5 10000 = 2 × 2 × 2 × 2 × 5 × 5 × 5 × 5

Step 3: Simplify the fraction by canceling out common prime factors: (5 × 5) / (2 × 2 × 2 × 2 × 5 × 5 × 5 × 5)

Step 4: The square root of 0.0025 is 0.05, as the prime factors align perfectly to form a perfect square.

The long division method is particularly used for non-perfect square numbers. However, it can also be used for perfect squares to verify results. Let us now learn how to find the square root using the long division method, step by step:

Step 1: Pair the decimal digits from left to right. The number 0.0025 is paired as 25 and 00.

Step 2: Find a number whose square is less than or equal to 25, which is 5, because 5 × 5 = 25.

Step 3: The quotient is 0.05, with a remainder of 0.

Step 4: Since we have no remaining digits, the square root of 0.0025 is 0.05.

The approximation method is another method for finding square roots, and 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 0.0025 using the approximation method.

Step 1: Identify the closest perfect squares around 0.0025. 0.0001 (√0.0001 = 0.01) and 0.01 (√0.01 = 0.1)

Step 2: Apply the approximation formula: (0.0025 - 0.0001) / (0.01 - 0.0001) = 0.25

Step 3: Adding the initial value to the approximation gives 0.01 + 0.04 = 0.05.

So the square root of 0.0025 is 0.05.

• Square root: A square root is the inverse of a square. Example: 0.05² = 0.0025 and the inverse of the square is the square root, that is √0.0025 = 0.05.
   
• 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.
   
• Perfect square: A perfect square is a number that is the square of an integer or a fraction. Example: 0.05² = 0.0025.
   
• Decimal: If a number has a whole number and a fraction in a single number, then it is called a decimal. For example, 0.05, 0.25, and 0.125 are decimals.
   
• Fraction: A fraction represents a part of a whole and is expressed as a ratio of two numbers, the numerator and the denominator. For example, 25/10000 is a fraction.