Radical Functions: Solving Radical Equations and Inequalities

think icon Think & Click: Solving Radical Inequalities

Now, you try. Complete the Think & Click activity by looking at each problem below, thinking about it, and then clicking on it to reveal the solution.

Solve square root of x is less than or equal to five
 

x ≥ 0

and

Square root of x is less than or equal to five. x is less than or equal to twenty five

0 ≤ x ≤ 25
 

Solve square root of the quantity x minus one is greater than two
 

x – 1 ≥ 0

x ≥ 1

and

Square root of the quantity x minus one is greater than two. x minus one is greater than four. x is greater than five

Since this is an "and" statement the two graphs of x ≥ 1 and x > 5 overlap starting at x > 5. Therefore, our final answer is x > 5.
 

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