Square Root of 1.04

The square root is the inverse of the square of the number. 1.04 is not a perfect square. The square root of 1.04 is expressed in both radical and exponential form. In the radical form, it is expressed as √1.04, whereas (1.04)^(1/2) in the exponential form. √1.04 ≈ 1.0198, 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 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. However, since 1.04 is a decimal, we can't directly apply prime factorization in the traditional sense used for integers. Thus, calculating 1.04 using prime factorization is not feasible.

The long division method is particularly used for non-perfect square numbers, including decimals. Let us now learn how to find the square root of 1.04 using the long division method, step by step:

Step 1: Consider 1.04 as 104 by moving the decimal two places to the right. Group the digits in pairs from right to left.

Step 2: Find a number whose square is less than or equal to 1. The number is 1. Subtract 1 from 1 to get a remainder of 0.

Step 3: Bring down the next pair of digits, which is 04, to make it 104. Double the current quotient (1), resulting in 2, and use it as the new divisor.

Step 4: Determine a digit n such that 2n × n ≤ 104. The suitable digit is 4.

Step 5: Subtract 104 from 104 to get a remainder of 0. Since we have reached the decimal point, place a decimal in the quotient.

Step 6: The quotient now is 1.0. Continue the process to refine the decimal places as needed.

The square root of 1.04 is approximately 1.0198.

The approximation method is another approach for finding square roots, especially for decimals. Let us learn how to find the square root of 1.04 using approximation:

Step 1: Identify the perfect squares around 1.04. The closest perfect squares are 1 (1^2) and 1.21 (1.1^2). Therefore, √1.04 is between 1 and 1.1.

Step 2: Use interpolation or successive approximation to refine the square root value. A rough estimate of the decimal value between 1 and 1.1 gives √1.04 ≈ 1.0198.

• Square root: A square root is the inverse of squaring a number. For example, 4² = 16, and the inverse operation is the square root: √16 = 4.

• Irrational number: An irrational number is a number that cannot be expressed as a fraction of two integers, such as √1.04.

• Decimal: A decimal is a number with a whole part and a fractional part separated by a decimal point, such as 1.04.

• Perfect square: A perfect square is a number that is the square of an integer, such as 4 (2²).

• Long division method: A technique used to find square roots of non-perfect squares by dividing the number into pairs of digits and determining the root step by step.