Algebra 2 · Unit 5 · Topic 5.2
Simplifying Radicals and Absolute Values
Simplify a real square root by extracting nonnegative perfect-square factors.
Definition and explanation
Simplify a real square root by extracting nonnegative perfect-square factors. For every real x, √(x²) = |x|, because a principal square root is nonnegative.
Worked example
Simplify √(72x²) for real x. Since 72x² = 36 × 2 × x², the result is 6|x|√2. At x = −1, both the original and simplified expressions equal 6√2.
Common mistake
Replacing √(x²) with x fails when x is negative.
Key takeaway
Simplify a real square root by extracting nonnegative perfect-square factors.
Explain each step of the worked example, then check the units, signs, and conditions that apply.
Further reading
Topic coverage was checked against the openly available OpenStax Intermediate Algebra 2e, Algebra and Trigonometry 2e, and Introductory Statistics 2e textbooks. The explanations and examples on this site are independently written; textbook prose, exercises, and artwork are not reproduced.