13.2 Simplifying Radicals

1. 13.2 Simplifying Radicals Teacher: If you add 20, 567, to 23, 678 and then divide by 97, what do you get? Jim: The wrong answer.

2. 13.2 Simplifying Radicals • Definitions: • Radicands: Expressions under radical signs • Radical: the square root (it is so rad!)

3. 13.2 Simplifying Radicals • 3 rules for simplifying radicals: • 1. NO radicands have perfect square factors other than 1 √8 = 2√2 • No radicands contain fractions. √3 = 1√3 √ 4 2 • No radicals appear in the denominator of a fraction. 1= 1 √4 2

4. 13.2 Simplifying Radicals • Properties of Radicals: • The square root of a product equals the product of the square roots of the factors. √ab = √a x √b • The square root of a quotient equals the quotient of the square roots of the numerator and denominator. √a/b = √a √b

5. 13.2 Simplifying Radicals • http://my.hrw.com/math06_07/nsmedia/homework_help/alg1/alg1_ch11_06_homeworkhelp.html (Professor Burger) Choose example 2, 3, and 4.

6. 13.2 Simplifying Radicals Example 1 √50 = √25 x 2 = √25 x √2 = 5√2 √3/4 = √3 √4 = √3 2

7. 13.2 Simplifying Radicals If the radical in a denominator is not the square root of a perfect square, then a different strategy is required.

8. 13.2 Simplifying Radicals Example 2 1/ √2 To simplify this expression, multiply the numerator and denominator by √2. (It is equivalent to multiplying the original fraction by 1)

9. 13.2 Simplifying Radicals 1/ √2 = 1√2 √2 √2 = __√2 . √2 √2 = √2 2

10. 13.2 Simplifying Radicals √2 inches √30 inches Example 3 Finding the area of a rectangle whose width is √2 inches and whose length is √30 inches. Give the result in exact form and in decimal form. bh = A √30 √2 √30(2) √60

11. 13.2 Simplifying Radicals The simplified form = √60 = √4 15 = √4 √15 = 2 √15 square inches Decimal approximation = √60 ≈ 7.75 square inches.

12. Assignment: 13-2 Page 652 1-23