Simplifying Radicals

1. Simplifying Radicals

2. Radical Flashback Simplifying Radicals: Find the greatest perfect square that goes into the radicand. Take the square root of the perfect square and keep the rest under the radical.

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4. Simplifying Square Roots with Variables • Variables with even exponents are perfect squares: 1. = because * remember when you multiply variables, you add exponents or * remember when you have a power to a power, you multiply the exponents

5. Simplifying Square Roots with Variables • Simplifying Perfect Squares: 2. = 4 because * 12 3. = 9 * 6 Note: The index of a square root is 2; therefore we divide the exponent by 2

6. Simplifying Square Roots with Variables • Simplifying Radicals that are NOT perfect squares = 3 Simplify the Variable: Note: The index of a square root is 2; therefore we divide the exponent by 2. Multiply the number and the variable for the final result: outside by outside – inside by inside

7. Simplifying Square Roots with Variables • Simplifying Radicals that are NOT perfect squares 2. = 5 Simplify the Variable: Divide the exponent by the index. The remainder stays under the radical. Multiply the number and the variable for the final result: outside by outside – inside by inside

8. Simplifying Square Roots with Variables 3. = 6 Simplify the Variable: Divide the exponent by the index. The remainder stays under the radical. Multiply the number and the variable for the final result: outside by outside – inside by inside

9. Simplifying Square Roots with Variables 4. = 6 Simplify the Variable: Divide the exponent by the index. The remainder stays under the radical. Multiply the number and the variable for the final result: outside by outside – inside by inside

10. Simplifying Square Roots with Variables 5. none Simplify the Variable: Divide the exponent by the index. The remainder stays under the radical. Multiply the number and the variable for the final result: outside by outside – inside by inside

11. Simplifying Square Roots with Variables 6. none Simplify the Variable: Divide the exponent by the index. The remainder stays under the radical. Multiply the number and the variable for the final result: outside by outside – inside by inside

12. Simplifying Square Roots with Variables 7. = 5 Simplify the Variables: Divide the exponent by the index. The remainder stays under the radical. Multiply the number and the variable for the final result: outside by outside – inside by inside

13. Simplifying Square Roots with Variables 8. = 3 Simplify the Variables: Divide the exponent by the index. The remainder stays under the radical. Multiply the number and the variable for the final result: outside by outside – inside by inside

14. Practice Time

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