Square Root of 0.0625

The square root is the inverse of the square of the number. 0.0625 is a perfect square. The square root of 0.0625 is expressed in both radical and exponential form. In the radical form, it is expressed as √0.0625, whereas (0.0625)^(1/2) in the exponential form. √0.0625 = 0.25, 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.

For perfect square numbers, the prime factorization method is often used. However, since 0.0625 is a decimal, we can simply convert it to a fraction and find its square root directly. Let us now learn the following methods:

• Fraction conversion method
• Direct calculation method

The fraction conversion method involves expressing the decimal as a fraction and then finding its square root.

Step 1: Convert 0.0625 to a fraction 0.0625 = 625/10000 = (25/100)²

Step 2: Find the square root of the fraction √(625/10000) = √(25²/100²) = 25/100 = 0.25

Thus, the square root of 0.0625 is 0.25.

The direct calculation method involves finding the square root of the decimal directly, as it is a straightforward calculation for perfect squares.

Step 1: Identify 0.0625 as a perfect square 0.0625 = (0.25)²

Step 2: Directly calculate the square root √0.0625 = 0.25

Thus, the square root of 0.0625 is 0.25.

Approximation methods are typically used for non-perfect squares, but here, we can verify the square root using an estimation approach.

Step 1: Consider numbers around 0.0625 The closest perfect square to 0.0625 is 0.04 (which is 0.2²) and 0.09 (which is 0.3²). √0.0625 falls between 0.2 and 0.3.

Step 2: Estimate more precisely Since 0.0625 is exactly halfway between 0.04 and 0.09, we can confirm √0.0625 is exactly 0.25.

• Square root: The square root is the inverse operation of squaring a number. Example: For 4² = 16, the square root is √16 = 4.
   
• Rational number: A rational number is a number that can be expressed as a fraction where both the numerator and the denominator are integers and the denominator is not zero. 
   
• Decimal: A decimal is a number that includes a decimal point, representing a fraction of a whole. For example, 0.25 represents 25/100.
   
• Perfect square: A perfect square is a number that is the square of an integer or a rational number. Example: 0.0625 is a perfect square because it equals (0.25)².
   
• Fraction: A fraction is a way to represent numbers by dividing one integer by another. Example: 0.0625 can be expressed as 625/10000.