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"Quadratic Radicals" Real Numbers PPT Courseware (Lesson 2)
Part One Content: Basic Knowledge Key Points
Knowledge point 1: Multiplication and division of quadratic radicals
1. The result of calculating √6a·√2a is (A)
A.2√3a B.√3/3
C.√3a D.√3a/3
2. (Adapted) Which of the following operations is correct (B)
A.2√7•3√7=6√7
B.√(4/3)=√4/√3=(2√3)/("( " √3 〖" )" 〗^2 )=(2√3)/3
C.√3/√9=√(3/9)=√(1/3)=3
D.√15÷√5×√3=√15÷√15=1
Knowledge point 2: Addition and subtraction of quadratic radicals
5. Which of the following calculations is correct (D)
A.√3+√2=√5 B.2+√2=2√2
C.2√6-√5=1 D.√8-√2=√2
6. Calculation: √48-2√3+7√75= 37√3.
Quadratic Radical PPT, Part 2: Improvement of Comprehensive Ability
11. If the integer part of √3 is x and the decimal part is y, then the value of √3x-y is (C)
A.3√3-3 B.√3
C.1 D.3
12. The following is the reasoning process by which A and B obtain √14+√6>√(14+6):
A: Because √14>√9=3, √6>√4=2, so √14+√6>3+2=5. And √(14+6)=√20<√25=5, so √ 14+√6>√(14+6).
B: Construct a right triangle. The lengths of the two right-angled sides are √14 and √6 respectively. Use the Pythagorean theorem to find that the square of the hypotenuse length is (√14)2+(√6)2=14+6, because the length of the hypotenuse is is greater than 0, so the length of the hypotenuse is √(14+6), because √14, √6, √(14+6) are the lengths of the three sides of the triangle, so √14+√6>√(14+6).
Regarding the reasoning between the two people, which of the following statements is correct (A)
A.Both are correct B.Both are wrong
C. A is correct, B is wrong D. A is wrong, B is correct
Quadratic Radical PPT, Part 3: Expansion, Research and Breakthroughs
17. If a+b=2, then a and b are said to be balanced numbers about 1.
(1)3 and -1 are equilibrium numbers about 1, 5-√2 and -3+√2 are equilibrium numbers about 1;
(2) It is known that m is an integer. If (m+√3)×(1-√3)=-5+3√3, determine whether m+√3 and 5-√3 are balanced numbers about 1, and explain the reason. .
Keywords: Beijing Normal University edition eighth grade mathematics PPT courseware free download, quadratic radical PPT download, real number PPT download, .PPT format;
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