A radical is an expression that involves a root, such as a square root (√) or cube root (∛). Simplifying radicals means rewriting them in a more manageable form by removing perfect squares or cubes from under the radical.
How to Simplify Radicals
- Factor the number under the radical and identify perfect squares (or cubes).
- Rewrite the radical by splitting it into two parts: a perfect square and another factor.
- Simplify the perfect square or cube outside the radical.
- Check your answer by squaring (or cubing) the simplified expression.
Examples
Example 1: Square Roots
Problem: Simplify √98
Step 1: Factor 98 → 98 = 49 × 2 (since 49 is a perfect square).
Step 2: Rewrite: √(49 × 2) = √49 × √2
Step 3: Simplify: 7√2
Final Answer: 7√2
Example 2: Cube Roots
Problem: Simplify ∛54
Step 1: Factor 54 → 54 = 27 × 2 (since 27 is a perfect cube).
Step 2: Rewrite: ∛(27 × 2) = ∛27 × ∛2
Step 3: Simplify: 3∛2
Final Answer: 3∛2
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