Table of contents
- 0. Review of College Algebra4h 43m
- 1. Measuring Angles39m
- 2. Trigonometric Functions on Right Triangles2h 5m
- 3. Unit Circle1h 19m
- 4. Graphing Trigonometric Functions1h 19m
- 5. Inverse Trigonometric Functions and Basic Trigonometric Equations1h 41m
- 6. Trigonometric Identities and More Equations2h 34m
- 7. Non-Right Triangles1h 38m
- 8. Vectors2h 25m
- 9. Polar Equations2h 5m
- 10. Parametric Equations1h 6m
- 11. Graphing Complex Numbers1h 7m
0. Review of College Algebra
Rationalizing Denominators
0. Review of College Algebra
Rationalizing Denominators: Study with Video Lessons, Practice Problems & Examples
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To rationalize a denominator with a single radical, multiply both the numerator and denominator by the radical. For example, to simplify
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concept
Rationalizing Denominators
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2mPlay a video:
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ProblemRationalize the denominator.
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ProblemRationalize the denominator.
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Rationalizing Denominators Using Conjugates
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ProblemRationalize the denominator and simplify the radical expression.
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ProblemRationalize the denominator and simplify the radical expression.
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PRACTICE PROBLEMS AND ACTIVITIES (89)
- CONCEPT PREVIEW Perform the operations mentally, and write the answers without doing intermediate steps. √25 ...
- CONCEPT PREVIEW Perform the operations mentally, and write the answers without doing intermediate steps. √6 •...
- CONCEPT PREVIEW Perform the operations mentally, and write the answers without doing intermediate steps. (√28...
- Find each square root. See Example 1. √100
- Find each square root. See Example 1. -√256
- Find each square root. See Example 1. √4⁄25
- Find each square root. See Example 1. -√144⁄121
- Find each square root. See Example 1. √-121
- Find the square of each radical expression. See Example 2. -√19
- Find the square of each radical expression. See Example 2. √2 3
- Find the square of each radical expression. See Example 2. √3x² + 4
- Find each root. See Example 3. -∛512
- Find each root. See Example 3. -∜16
- Find each root. See Example 3. ∛0.001
- Find each root. See Example 3. ∛0.125
- Use the product and quotient rules for radicals to rewrite each expression. See Example 4. √3 • √5
- Use the product and quotient rules for radicals to rewrite each expression. See Example 4. √3 • √27
- Use the product and quotient rules for radicals to rewrite each expression. See Example 4. √7⁄16
- Use the product and quotient rules for radicals to rewrite each expression. See Example 4. √4⁄50
- Use the product and quotient rules for radicals to rewrite each expression. See Example 4. √5 √20
- Use the product and quotient rules for radicals to rewrite each expression. See Example 4. 30√10 5√2
- Simplify each radical. See Example 5. √24
- Simplify each radical. See Example 5. √75
- Simplify each radical. See Example 5. - √160
- Simplify each radical. See Example 5. 3√27
- Add or subtract, as indicated. See Example 6. 2√3 + 5√3
- Add or subtract, as indicated. See Example 6. 5√3 - √3
- Add or subtract, as indicated. See Example 6. √6 + √6
- Add or subtract, as indicated. See Example 6. √6 + √7
- Add or subtract, as indicated. See Example 6. 5√3 + √12
- Add or subtract, as indicated. See Example 6. √45 + 4√20
- Add or subtract, as indicated. See Example 6. 2√50 - 5√72
- Add or subtract, as indicated. See Example 6. -5√32 + 2√98
- Multiply. See Example 7. √6 (3 + √2)
- Multiply. See Example 7. (√2 + 1) (√3 + 1)
- Multiply. See Example 7. (√2 - √3) (√2 + √3)
- Multiply. See Example 7. (√5 + 2)²
- Rationalize each denominator. See Example 8. 6 —— √5
- Rationalize each denominator. See Example 8. 5 —— √5
- Rationalize each denominator. See Example 8. 4 —— √6
- 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 nume...
- For Individual or Group Work (Exercises 147 – 150)In calculus, it is sometimes desirable to rationalize a nume...
- 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
- Find the domain of each rational expression. See Example 1. x + 3 x - 6
- Find the domain of each rational expression. See Example 1. 3x + 7 ——————— (4x + 2) (x - 1)
- Find the domain of each rational expression. See Example 1. 12 —————— x² + 5x + 6
- Find the domain of each rational expression. See Example 1. x² - 1 ———— x + 1
- Find the domain of each rational expression. See Example 1. x³ - 1 ———— x - 1
- Write each rational expression in lowest terms. See Example 2. 8x² + 16x 4x²
- Write each rational expression in lowest terms. See Example 2. 3 (3 - t) —————— (t + 5) (t - 3)
- Write each rational expression in lowest terms. See Example 2. 8k + 16 9k + 18
- Write each rational expression in lowest terms. See Example 2. m² - 4m + 4 m² + m - 6
- Write each rational expression in lowest terms. See Example 2. 8m² + 6m - 9 16m² - 9
- Multiply or divide, as indicated. See Example 3. 15p³ 12p —— • ——— 9p² 10p³
- Multiply or divide, as indicated. See Example 3. 2k + 8 3k + 12 ———— ÷ ———— 6 2
- Multiply or divide, as indicated. See Example 3. x² + x 25 ———— • ———— 5 xy + y
- Multiply or divide, as indicated. See Example 3. 4a + 12 a² - 9 ————— ÷ ————— 2a - 10 a² - a - 20
- Multiply or divide, as indicated. See Example 3. m² + 3m + 2 m² + 5m + 6 ——————— ÷ ———————— m² + 5m + 4 m² ...
- Add or subtract, as indicated. See Example 4. 3 5 —— + —— 2k 3k
- Add or subtract, as indicated. See Example 4. 1 2 4 —— + —— + —— 6m 5m m
- Add or subtract, as indicated. See Example 4. 1 b —— + —— a a²
- Add or subtract, as indicated. See Example 4. 5 11 ———— - ——— 12x²y 6xy
- Add or subtract, as indicated. See Example 4. 17y + 3 -10y - 18 ———— - ————— 9y + 7 9y + 7
- Add or subtract, as indicated. See Example 4. 1 1 ——— + ——— x + z x - z
- Add or subtract, as indicated. See Example 4. 3 1 ——— - ——— a - 2 2 - a
- Add or subtract, as indicated. See Example 4. x + y 2x ——— - ——— 2x - y y - 2x
- Add or subtract, as indicated. See Example 4. 4 1 12 ———— + —————— - ———— x + 1 x² - x + 1 x³ + 1
- Add or subtract, as indicated. See Example 4. 3x x —————— - ———— x² + x - 12 x² - 16
- Simplify each complex fraction. See Examples 5 and 6. 4 - — 3 ———— 2 — 9
- Simplify each complex fraction. See Examples 5 and 6. y r —— x r
- Simplify each complex fraction. See Examples 5 and 6. 5⁄8 + 2⁄3 ———— 7⁄3 - 1⁄4
- Simplify each complex fraction. See Examples 5 and 6. ( -4⁄3 ) + 12⁄5 ———————— 1 - ( -4⁄3 ) (12⁄5)
- Simplify each complex fraction. See Examples 5 and 6. 1 + 1 x ———— 1 - 1 x
- Simplify each complex fraction. See Examples 5 and 6. x y — + — y x —————— x y — - — y x
- Simplify each complex fraction. See Examples 5 and 6. 1 1 ——— - —— x + 1 x ———————— 1 —— x
- Simplify each complex fraction. See Examples 5 and 6. y + 3 4 ———— - ———— y y - 1 —————————— y 1 ——— + —...
- (Modeling) Distance from the Origin of the Nile River The Nile River in Africa is about 4000 mi long. The Nile...