Mastering Adding and Subtracting Radicals: A Simplification Guide

1. Unit 1 Relationships Between Quantities and ExpressionsWeek 2Lesson 2 – Add/Subtract Radicals (restricted to square roots only)

2. Today’s Objective • MGSE9-12.N.RN.2 Rewrite expressions involving radicals (restricted to square roots only) • MGSE9-12.N.RN.3 Explain why the sum or product of rational numbers is rational; why the sum of a rational number and an irrational number is irrational; and why the product of a nonzero rational number and an irrational number is irrational. • Objective: Students will Add, Subtract and Simplify radical expressions

3. Essential Questions • If you add two radicals will you always get another radical? • If you add two irrationals numbers will you get another irrational number? • How do you simplify a radical expression?

4. Vocabulary • Simplify • Like Terms • Radicals • Radicands • Simplest Form • Factors

5. Read, Write, Draw, Solve There are a list of numbers below. Sort the numbers in order from least to greatest and explain your thought process.

6. Sums and Differences Rules in the previous section allowed us to split radicals that had a radicand which was a product or a quotient. We can NOT split sums or differences.

7. When ADDING and SUBTRACTING Square Roots…..it is very similar to ADDING and SUBTACTING LIKE TERMS. Just as you ADD the LIKE TERM of X…. COEFFICIENTS You ADD the LIKE TERM of …. LIKE TERMS

8. Adding and Subtracting Square Roots Flow Chart Make sure all Square Roots are in Simplest Form. Simplify all Square Roots Check for LIKE TERMS Add/Subtract the COEFFICIENTS ONLY ADD or SUBTRACT Terms that have the SAME Square ROOT! Once you Combine Like Terms, You place the new Coefficient in front of The Square Root.

9. A. Adding and Subtracting Square-Root Expressions Add or subtract. The terms are like radicals. B. The terms are unlike radicals. Do not combine.

10. a. b. Try This! Add or subtract. The terms are like radicals. The terms are like radicals.

11. Sometimes radicals do not appear to be like until they are simplified, Simplify all radicals in an expression before trying to identify like radicals.

12. Simplify Before Adding or Subtracting Simplify each expression. Factor the radicands using perfect squares. Product Property of Square Roots. Simplify. Combine like radicals.

13. Simplify Before Adding or Subtracting Simplify each expression. Factor the radicands using perfect squares. Product Property of Square Roots. Simplify. The terms are unlike radicals. Do not combine.

14. Try This! Simplify each expression. Factor the radicands using perfect squares. Product Property of Square Roots. Simplify. Combine like radicals.

15. Try This! Simplify each expression. Factor the radicands using perfect squares. Product Property of Square Roots. Simplify. The terms are unlike radicals. Do not combine.

16. Geometry Application Find the perimeter of the triangle. Give the answer as a radical expression in simplest form. Write an expression for perimeter. Factor 20 using a perfect square. Product Property of Square Roots. Simplify. Combine like radicals.

17. You try these!

18. Find the perimeter of a rectangle whose length is inches and whose width is inches. Give your answer as a radical expression in simplest form. Draw it How do you find the perimeter?

19. Write an expression for perimeter 2 (l + w). Multiply each term by 2 . Simplify. Combine like radicals.

20. Exit Ticket • Find the perimeter of the trapezoid. Give the answer as a radical expression in simplest form.