Square Root of 0.0004

The square root is the inverse of the square of a number. 0.0004 is a perfect square, and its square root can be expressed in both radical and exponential form. In radical form, it is expressed as √0.0004, whereas in exponential form, it is expressed as (0.0004)^(1/2). The square root of 0.0004 is 0.02, which is a rational number because it can be expressed as a fraction p/q, where p and q are integers and q ≠ 0.

For finding the square root of perfect square numbers, the prime factorization method is used. Since 0.0004 is a perfect square, we can also use simple arithmetic analysis. Let's explore the methods:

• Prime factorization method
• Simple arithmetic method

The prime factorization method involves breaking down a number into its prime factors. Let's look at how 0.0004 is broken down:

Step 1: Express 0.0004 as a fraction: 0.0004 = 4/10000.

Step 2: Simplify the fraction: 4/10000 = 1/2500.

Step 3: The prime factors of 2500 are 2² × 5⁴.

Step 4: Take the square root of each factor: √(1/2500) = 1/(2 × 5²) = 1/50.

Step 5: The square root of 0.0004 is 0.02.

The simple arithmetic method is straightforward for perfect squares. Here's how you can find the square root of 0.0004:

Step 1: Recognize that 0.0004 is 4/10000.

Step 2: Note that 4 is a perfect square (2 × 2), and 10000 is a perfect square (100 × 100).

Step 3: Therefore, √(4/10000) = 2/100 = 0.02.

So, the square root of 0.0004 is 0.02.

Students often make mistakes while finding square roots, such as using incorrect methods or ignoring negative roots. Let's explore some common mistakes and how to avoid them.

• Square root: The square root of a number is a value that, when multiplied by itself, gives the original number. Example: √0.0004 = 0.02.
   
• Rational number: A rational number is a number that can be expressed as a fraction p/q, where p and q are integers and q ≠ 0.
   
• Perfect square: A perfect square is a number that is the square of an integer. Example: 4 is a perfect square because it is 2².
   
• Decimal: A decimal is a number that has a whole number part and a fractional part separated by a decimal point, such as 0.02.
   
• Fraction: A fraction represents a part of a whole and is expressed as p/q, where p is the numerator and q is the denominator.