Steps:

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

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

First example (click here):

Step 1: Isolate the square root

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

Step 4: Simplify and compute the inequality

Step 5: Combine the ranges

and

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

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