Square Root of 0.05

The square root is the inverse of the square of a number. 0.05 is not a perfect square. The square root of 0.05 is expressed in both radical and exponential form. In radical form, it is expressed as √0.05, whereas (0.05)^(1/2) in the exponential form. √0.05 ≈ 0.2236, 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, the prime factorization method is not used for non-perfect square numbers where long-division and approximation methods 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. Since 0.05 is not a whole number, we cannot directly use prime factorization in the traditional sense. Instead, we convert to a fraction:

Step 1: Express 0.05 as a fraction: 0.05 = 5/100 = 1/20

Step 2: Prime factorize 20: 20 = 2 x 2 x 5

Step 3: Therefore, √0.05 = √(1/20) = √(1/(2² x 5)) = 1/(2√5)

The long division method is particularly used for non-perfect square numbers. Let us now learn how to find the square root using the long division method, step by step.

Step 1: First, convert 0.05 to 5/100 and then to 0.05 for division.

Step 2: Group the digits from right to left. Here, we'll work with 0.0500, grouping as 05 and 00.

Step 3: Find a number whose square is less than or equal to the first group (05). That number is 2, as 2 x 2 = 4.

Step 4: Subtract 4 from 5, giving a remainder of 1.

Step 5: Bring down the next two zeros, making the new dividend 100.

Step 6: Double the divisor (which is 2), making it 4.

Step 7: Determine the next digit in the quotient (n), such that 4n x n ≤ 100. The number is 2, as 42 x 2 = 84.

Step 8: Subtract 84 from 100 to get 16, and bring down another pair of zeros.

Step 9: Continue this process until the desired accuracy is achieved.

The approximation method is another method for finding square roots, which is an easy way to find the square root of a given number. Let's see how to find the square root of 0.05 using the approximation method.

Step 1: Identify the perfect squares closest to 0.05. The perfect squares are 0.04 (√0.04 = 0.2) and 0.09 (√0.09 = 0.3).

Step 2: Apply the formula: (Given number - smallest perfect square) / (Greater perfect square - smallest perfect square) Using the formula: (0.05 - 0.04) / (0.09 - 0.04) = 0.01 / 0.05 = 0.2 Adding the value to the initial smaller root: 0.2 + 0.2 = 0.22.

So the square root of 0.05 is approximately 0.22

• Square root: A square root is the inverse of a square. For example, 0.2² = 0.04, and the inverse of the square is the square root, that is, √0.04 = 0.2.
   
• Irrational number: An irrational number is one that cannot be written in the form of p/q, where q is not equal to zero and p and q are integers.
   
• Decimal: A decimal is a number that has a whole number and a fractional part separated by a decimal point, such as 0.05.
   
• Radical form: Expressing a number under a square root symbol, such as √0.05, is called radical form.
   
• Exponential form: Expressing a number with a fractional exponent, such as (0.05)^(1/2), is called exponential form.