0. Review of College Algebra

Rationalize each denominator. See Example 8. 18—— √27

Rationalize each denominator. See Example 8. 12—— √72

Rationalize each denominator. See Example 8. 3———— 4 + √5

Rationalize each denominator. See Example 8. 6———— √5 + √3

Rationalize each denominator. See Example 8. √3 + 1———— 1 - √3

Rationalize each denominator. See Example 8. √2 - √3———— √6 - √5

Simplify. See Example 9. - √2 3——— √7 3

Simplify. See Example 9. √7 5——— √3 10

Simplify. See Example 9. 1 2———1 - √5 2

Simplify. See Example 9. √3 2———1 - √3 2

For Individual or Group Work (Exercises 147 – 150)In calculus, it is sometimes desirable to rationalize a numerator. To do this, we multiply the numerator and the denominator by the conjugate of the numerator. For example,6 - √2 = 6 - √2 • 6 + √2 = 36 - 2 = 34 = 17 . 4 4 6 + √2 4(6 + √2) 4(6 + √2) 2(6 + √2)Rationalize each numerator.6 - √3 8

For Individual or Group Work (Exercises 147 – 150)In calculus, it is sometimes desirable to rationalize a numerator. To do this, we multiply the numerator and the denominator by the conjugate of the numerator. For example,6 - √2 = 6 - √2 • 6 + √2 = 36 - 2 = 34 = 17 . 4 4 6 + √2 4(6 + √2) 4(6 + √2) 2(6 + √2)Rationalize each numerator.2√10 + √7 30

CONCEPT PREVIEW Perform the indicated operation, and write each answer in lowest terms 2x 10x—— • ——— 5 x²

CONCEPT PREVIEW Perform the indicated operation, and write each answer in lowest terms 3 7—— + —— x x

CONCEPT PREVIEW Perform the indicated operation, and write each answer in lowest terms 2x x—— + —— 5 4