Cornell Notes Template - Algebra with Ms. Simmons



Name _________________ Section _____ Date: Monday, August 23, 2010

Cornell Notes: Simplifying Radical Expressions

|Key Vocabulary |Radicand, radical expression, rationalizing the denominator, radical equation, extraneous solution, |

|Vocabulary/Definitions |A Radical Expression is an expression that contains a radical such as a square root, cube root, or other root. |

| |A Radical Function is a radical expression that contains an independent variable IN the radicand. |

| |An example would be y = x + 2 |

| |Rationalizing the Denominator is the process of eliminating a radical from an expression’s denominator. |

| |Radical Equation is an equation that contains a radical expression with a variable in the radicand. |

| |Extraneous Solution is a solution or answer that does not fit into the original equation. |

| | |

| |Three (3) ways to simplify radical expressions |

| |Look for perfect square factors in the radicand |

| |Eliminate radicals in the denominator of a fraction (Rationalizing the denominator) |

| |Eliminate fractions in the radicand |

| |A radical is in simplest form when the following are true: |

|Simplifying Radical Expressions |No perfect square factors other than 1 are in the radicand |

| |No fractions are in the radicand |

| |No radicals appear in the denominator of a fraction. |

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| |Product Property of Radicals |

| |Explanation: The square root of a product equals the product of the square roots of the factors. |

| |Algebra terms: _______ = _______ x ________ |

| |Example: |

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|Properties of Radicals |32 = 16 x 2 |

| |= 16 x 2 |

| |= 4 2 |

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| |Let’s Practice! |

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| |Quotient Property of Radicals |

| |Explanation: The square root of a quotient equals the quotient of the square roots of the numerator and denominator. |

| |Algebra terms: __________ = __________ |

| |Example |

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| |Let’s Practice |

|Rationalize the Denominator |Rationalizing the Denominator is the process of eliminating a radical from an expression’s denominator. |

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|Add or Subtract Radicals |You can use the distributive property to simplify sums and differences of radical expressions when the expressions have |

| |the same radicand. |

| |Example: |

|Things to Remember |Remember that different radicals, the same as Like Terms, cannot be added or subtracted but can be multiplied and |

| |divided. |

| |Example: |

|Try these for Practice | |

Yes my scholar has reviewed these notes and understands how to successfully divide and multiply decimals. We have worked the sample problems attached. Signing below means I acknowledge that my scholar will master this skill and get a 5 point bonus added to the assessment IF she/he passes the assessment.

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(Parent/Guardian Signature- 5 point bonus)

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