"Quadratic Radicals" Real Numbers PPT Courseware (Lesson 1)

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"Quadratic Radicals" Real Numbers PPT Courseware (Lesson 1)

Part One Content: Basic Knowledge Key Points

Knowledge point 1: The concept of quadratic radicals

1. The following formula:√7,√2x,√(1"-" m),√(a^2+b^2 ),√100,√(a^2 "-" 1),√("& #124;" a"|" +1), there must be a quadratic radical (B)

A.3 B.4

C.5 D.6

2. If √("-" 2m+1) is meaningful, then the maximum integer value that m can take is (B)

A.-1 B.0 C.1 D.2

Knowledge point 2: The simplest quadratic radical

3. Among the following formulas, the simplest quadratic root formula is (D)

A.√27 B.√(m^5 n^2)

C.√(1/2) D.√6

4. Convert √(4/3) into the simplest quadratic radical, and the result is (2√3)/3.

Quadratic Radical PPT, Part 2: Improvement of Comprehensive Ability

8. If a<0, b<0, and a-b=6, then the value of √(a^2)-√(b^2) is (B)

A.6 B.-6

C.6 or -6 D. Unable to determine

9. Among the following quadratic radicals, which one is not the simplest quadratic radical (A)

A.√(3/4) B.√47

C.(9√3)/2 D.2√2

10. If (m-1)2+√(n+2)=0, then m+n= -1　.

11. (Adaptation) It is known that y=√(3x"-" 1)+√(1"-" 3x)+√("( " x"-" 1〖" )" 〗^2 ), then ( x+ 4y )3=　27　.

[Variation expansion] If a and b are both real numbers, and b=√(1"-" 2a)+√(2a"-" 1)-2, then the value of ab is 4.

Quadratic Radical PPT, Part 3: Expansion, Research and Breakthroughs

14. Reading materials: After learning the quadratic radical formula, Xiao Ming found that some formulas containing radicals can be written as the square of another formula, such as 3+2√2=(1+√2)2. Xiao Ming, who is good at thinking, carried out Exploring the following:

Suppose a+b√2=(m+n√2)2 (where a, b, m, n are all positive integers), then a+b√2=m2+2n2+2mn√2,∴a=m2 +2n2,b=2mn. In this way, Xiao Ming found a way to convert part of the formula a+b√2 into a square form.

Please follow Xiao Ming’s approach to explore and solve the following problems:

(1) When a, b, m, and n are all positive integers, if a+b√3=(m+n√3)2, use formulas containing m and n to express a and b respectively, and get a= m2+3n2　,b= 2mn　;

(2) Use the explored conclusions to find a set of positive integers a, b, m, n and fill in the blanks: 4+2 √3=( 1+1 √3 )2;

(3) Simplification:√(14+6√5) =　3+√5　.

Keywords: Beijing Normal University edition eighth grade mathematics PPT courseware free download, quadratic radical PPT download, real number PPT download, .PPT format;

For more information about the "Quadratic Radicals of Real Numbers" PPT courseware, please click on the Real Numbers PPT Quadratic Radicals PPT tab.

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Update Time: 2024-07-29

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