Square Root Function

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Square root function is a function which is represented with the radical sign ‘√’. Inside a square root, a number or an expression can be placed and we can find the square root of it. The parent function or the basic square root function is y = √x and here ‘y’ is the function value also known as f(x) and ‘x’ is the variable. All other square root functions can be derived from this parent function and can be graphed on the X-Y coordinate plane.

Example 1: Given the square root function, f(x) = √(5x). Find the function value when x is equal to 4.

Given square root function: f(x) = √(5x)

In order to find the function value or the ‘y’ value at x = 4, we substitute x = 4 in the above square root function.

This gives: y = f(4) = √(5 * 4) = √20.

We can simplify √20 by writing its prime factors==> √20 = √(2* 2* 5) = 2√5.

Therefore √20 or 2√5 is the function value at x = 4.

Example 2: Given the square root function, f(x) = √(x + 6). Find the function value when x is equal to 3.

Given square root function: f(x) = √(x + 6)

In order to find the function value or the ‘y’ value at x = 3, we substitute x = 3 in the above square root function.

This gives: y = f(3) = √(3 + 6) = √9.

‘9’ is a perfect square since 9 can be written as 3 * 3.

Hence √9 = √(3 * 3) = 3

Therefore ‘3’ is the function value when x = 3.