"Mixed Operations of Quadratic Radical Expressions" Quadratic Radical Expression PPT Courseware

Description

"Mixed Operations of Quadratic Radical Expressions" Quadratic Radical Expression PPT Courseware

When two algebraic expressions containing quadratic radicals are multiplied together, if their product does not contain a quadratic radical, we say that these two algebraic expressions containing quadratic radicals are rational factors of each other.

For example: the rationalization factor of √(x+y) is √(x+y)

The rationalization factor of √x+√y is √x-√y

The rationalization factor of a√x-b√y is a√x+b√y

1. Rational basic method of denominator

Exercise 1/(√3+√2)+1/(√2+1)-2/(√3+1)

2. Decomposition and reduction method

Simplify x-y/√x+√y Exercise (x+2√xy+y/√x+√y)+(x-y/√x+√y)

question

How to calculate the following equation? Does the observed product contain a quadratic radical?

(√x+√y)(√x-√y)=x-y

When two non-zero algebraic expressions containing quadratic radicals are multiplied together, if their product does not contain a quadratic radical, the two non-zero algebraic expressions containing quadratic radicals are said to be rational factors of each other.

√x+√y and √x-√y are rational factors of each other.

think about it

The rationalized factor of a+√b is a-√b;

The rationalized factor of √a+b is √a+b;

The rationalization factor of a√x+b√y is a√x-b√y;

The rationalized factor of a√b is √b.

Compare the sizes of radicals.

√6+√14 and √7+√13

Explore:

(1)

Given that x=√3, find the value of the algebraic formula (x-2)²-(x-2)(x+2)+2√3

(2) It is known that a=3+2√5, b=3-2√5, find the value of a²b-ab²

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For more information about the PPT courseware "Mixed Operations of Quadratic Radicals and Quadratic Radicals", please click the Mixed Operations of Quadratic Radicals ppt Quadratic Radicals ppt tag.

"Mixed Operations of Quadratic Radicals" PPT courseware:

"Mixed Operations of Quadratic Radicals" PPT courseware What characteristics do they have to be combined in order to perform addition and subtraction operations of quadratic radicals? (1) Name three quadratic radicals of the same kind for 25; (2) Try to name a group of quadratic radicals of the same kind. (3) Which of the following formulas are quadratic radicals of the same kind?

"Mixed Operations of Quadratic Radicals" Quadratic Radicals PPT Courseware 2:

"Mixed Operations of Quadratic Radical Expressions" Quadratic Radical Expression PPT Courseware 2 Clarify the learning objectives 1. Multiplication and division operations of formulas containing quadratic radicals and the application of polynomial multiplication formulas containing quadratic radicals. 2. Review the knowledge of integer operations and apply this knowledge to...

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Update Time: 2024-11-20

This template belongs to Mathematics courseware People's Education Press Eighth Grade Mathematics Volume 2 industry PPT template

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