High School Math Solutions – Inequalities Calculator, Radical Inequalities

Last post, we went over how to solve absolute value inequalities. For today’s post, we will talk about how to solve radical inequalities. Solving radical inequalities is easier than solving absolute value inequalities and require fewer steps. Let’s see the steps on how to solve these inequalities.

Steps:

1. Isolate the square root
2. Check that the inequality is true (i.e. not less than 0)
3. Find the real region for the square root, (i.e. see when the expression inside square root is greater than or equal to 0)
4. Simplify and compute the inequality
5. Combine the ranges

Let’s see how to do one example step by step.

First example (click here):

                                                                    \sqrt{5+x}-1<3

Step 1: Isolate the square root

                                                                    \sqrt{5+x}<4

Step 2: Check that the inequality is true

Yes, this inequality is true the radical is not less than 0.

Step 3: Find the real region for the square root

                                                                       5+x≥0

                                                                         x≥-5

Step 4: Simplify and compute the inequality

                                                                    \sqrt{5+x}<4

                                                                (\sqrt{5+x})^2<4^2

                                                                     5+x<16

                                                                       x<11
Step 5: Combine the ranges

                                                                  x≥-5 and x<11

                                                                     -5≤x<11

That wasn’t too difficult. Let’s see some more examples.

Second example (click here):

Last example (click here):

Solving radical inequalities isn’t too difficult, however, they require practice. For more practice examples check out Symbolab’s practice.

Until next time,

Leah