Mastering The Square Root Function: A Step-By-Step Guide For Calculating Non-Negative Real Numbers

Square Root Function

f(x) = √x

The square root function is a mathematical function that takes an input value and returns the positive value of the square root of that input value. It can be represented using the symbol √.

The square root function is denoted as f(x) = √x. The value of x is referred to as the input, while the value of √x is referred to as the output. The domain of the square root function is all non-negative real numbers, while the range is all non-negative real numbers greater than or equal to zero.

To determine the value of the square root of a given number, we can use a calculator or manually solve using the following steps:

1. Estimate the perfect square that is closest to the given number.
2. Divide the number by the estimated perfect square.
3. Average the result of step 2 with the estimated perfect square.
4. Repeat steps 2 and 3 until the answer reaches the desired accuracy.

For example, to find the square root of 25, the estimated perfect square is 16. We then divide 25 by 16 to get 1.5625. We average 16 and 1.5625 to get 8.78125, and repeat the process until the desired accuracy is reached. The square root of 25 is 5.

The square root function is commonly used in various fields such as engineering, physics, and statistics. It is also a fundamental concept in the study of algebra and calculus.

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