Simplifying Radical Expressions
Simplify radical expressions using the Product Property by factoring out perfect squares. Write radicals in simplest form for Grade 9 algebra.
Key Concepts
New Concept If $a$ and $b$ are non negative real numbers, then: $$ \sqrt{a} \sqrt{b} = \sqrt{ab} \quad \text{and} \quad \sqrt{ab} = \sqrt{a} \sqrt{b} $$ What’s next Next, you’ll apply this rule to simplify radicals using perfect squares, prime factors, and variables to solve problems.
Common Questions
How do you simplify a radical using the Product Property?
Factor the radicand to find perfect square factors, then split using sqrt(ab) = sqrt(a) times sqrt(b). For sqrt(72), write sqrt(36 times 2) = 6sqrt(2).
What is the Product Property of Radicals?
sqrt(a) times sqrt(b) = sqrt(ab) for non-negative a and b. This works in both directions: you can split a radical or combine two radicals into one.
When is a radical expression fully simplified?
When the radicand has no perfect square factors, no fractions under the radical, and no radicals in the denominator.