Warm-Up: HW #5: Simplifying radicals Agenda WU (10 min) SWBAT…simplify radicals using the product property of radicals Wed, 3/14 Agenda WU (10 min) Lesson on product property of radicals – 13 examples! (30 min) Warm-Up: HW #5: Simplifying radicals

Simplifying Radical Expressions

Properties of Radicals

In the expression , is the radical sign and 64 is the radicand.

What numbers are perfect squares? 1 • 1 = 1 2 • 2 = 4 3 • 3 = 9 4 • 4 = 16 5 • 5 = 25 6 • 6 = 36 49, 64, 81, 100, 121, 144, ...

Product Property of Radicals (13 examples)

Product Property of Radicals For any numbers a and b where and ,

1. Simplify

Find a perfect square that goes into 147. 2. Simplify Find a perfect square that goes into 147.

3. Simplify

Find a perfect square that goes into 605. 4. Simplify Find a perfect square that goes into 605.

5. Simplify .

6. Simplify 6b. Simplify As a general rule, divide the exponent by two. The remainder stays in the radical.

7. Simplify

8. Simplify As a general rule, divide the exponent by two. The remainder stays in the radical.

9. Simplify As a general rule, divide the exponent by two. The remainder stays in the radical.

10. Simplify 3x6 3x18 9x6 9x18 As a general rule, divide the exponent by two. The remainder stays in the radical.

11. Simplify Multiply the radicals.

Multiply the coefficients and radicals. 12. Simplify Multiply the coefficients and radicals.

13. Simplify .

SWBAT…simplify radicals using the quotient of property of radicals Agenda WU (10 min) Lesson on quotient property of radicals – 5 examples (20 min) Lesson on adding and subtracting radicals – 6 examples (15 min) Warm-Up: 1. HW #7: Quotient Property of Radicals

Quotient Property of Radicals (5 examples)

Quotient Property of Radicals For any numbers a and b where and ,

Examples:

Rationalizing the denominator Rationalizing the denominator means to remove any radicals from the denominator. 3. Simplify

4. Simplify

Simplify 5.

How do you know when a radical problem is done? No radicals can be simplified. Example: There are no fractions in the radical. Example: There are no radicals in the denominator. Example:

    = 6     = 3   = 2

Adding and Subtracting Radicals (6 examples)

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

Adding and Subtracting Radicals We can only combine terms with radicals if we have like radicals Ex 1 Ex 2 Ex 3 Simplified

Adding and Subtracting Radicals Ex 4

Adding and Subtracting Radicals Ex 5 Simplify the following radical expression.

Ex 6