Similar to rational expressions, there are values that will cause a radical expression to be undefined

Question

Similar to rational expressions, there are values that will cause a radical
expression to be undefined. Discuss the concept of an undefined radical
expression (when will this occur and how do you find the values) and provide an
example

Answer 1

Radical expression contains a square root (√) of some expression. It undefined when value inside radical (called discriminant) is negative.

Square root is not defined for negative values of discriminant. It is defined only for all values of discriminant that are greater than or equal to zero (>= 0).

So undefined radical expression will occur when the value of discriminant (value inside radical) is negative.

We find the value when radical is undefined by setting the value of discriminant to less than zero (< 0).

e.g. √(3x - 6) is undefined when discriminant 3x - 6 < 0. Here we need to find value of x when radical is undefined.

3x - 6 <  0.....add 6 to both sides

3x - 6 + 6 < 0 + 6

3x < 6....to simplify, we divide both sides by 3

3x/3 < 6/3

x < 2

So above radical expression, √(3x - 6), is undefined when x < 2.

check:

when x = 1, √(3.1 - 6) = √(3 - 6) = √-3 .....square root of a negative number is undefined and so radical expression is undefined for x = 1.

when x = 2, √(3.2 - 6) = √(6 - 6) = √0 = 0 .....So for 2 radical expression is defined (= 0).