Simplifying Radical Expressions
Simplify radical expressions in Grade 10 algebra. Apply the product rule for radicals, factor out perfect square pairs, and write expressions in simplest radical form.
Key Concepts
New Concept The Product Rule for Radicals: $\sqrt[n]{ab} = \sqrt[n]{a} \cdot \sqrt[n]{b}$ and $\sqrt[n]{a} \cdot \sqrt[n]{b} = \sqrt[n]{ab}$.
What’s next Next, you'll apply this rule to simplify and combine radical expressions, including those with variables.
Common Questions
How do you simplify a radical expression using the product rule?
Factor the radicand to find the largest perfect square factor. Write as a product of radicals: √(a·b) = √a · √b. Evaluate √a and leave √b simplified under the radical.
How do you simplify √72?
Find the largest perfect square factor: 72 = 36 × 2. So √72 = √36 · √2 = 6√2. Always use the largest perfect square to minimize steps.
What does simplest radical form mean?
A radical is in simplest form when: no perfect square factors remain under the radical, no fractions appear under the radical, and no radicals appear in the denominator.