Chapter 21 Quadratic Radicals Full Chapter Study Plans and Test Question Answers

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（1）√24×√27 （2）√6×（-15） （3）√18×√20×√75

Solution: Original=2 6 3 3 Solution: Original=- 6 15 Solution: Original=3 2 2 5 5 3

2.Simplify. Solution: Original = 2 49 Solution: Original = (3 100).

Because x-1 0, 1-x 0

So x-1=0, x=1

Substituting x=1 into the original formula gives y=-1

So x-y=1-(-1)=2

Solution:

Original = (1 2 3) 2 1 3) (1 2 5) = (1 2 3 2 1 1 2 5) = (5 3 7 3 7 5).

Solution: Original = (3a) 3 (a 2) 1 2 (2a 3) = (1 3 1 2) 3a a 2 2a 3) = 1 6 (3a 2 a 2a 3).

1/6×√(4a²)

1/6×2a

A 3 Solution:

Original = 2 (1 8)- 1 2)-[18+ 2-2 (1 3)]=2 (1 8)- 1 2)- 18- 2+2 (1 3)=2 (2 4 )-2 2 )-3 2)- 2+2 (3 3).

Solution: Original = [ ( ( 8 27)-5 3] 6

Solution: Original formula = (2 3-2) (3 6 + 2).

Simplification: A -1 0 1 b can be seen from the number line

a+1﹤0 , b-1﹥0, a-b﹤0√(a+1)²+b-1)²-a-b|=|a+1|+|b-1|-|a-b|

(a+1)+b-1+(a-b)

a-1+b-1+a-b=-2

1.Propose ab and become ab(a2-b 2), and use the square difference formula to convert to ab(a+b)(a-b), where ab is 1 and (a+b)(a-b) is 24 times the root number 2So the original formula = 24 times the root number 2

2.The square difference formula for the common denominator is (y 2)x-(x 2)y, and the square difference is also used for the denominator, which is simplified to 2 (x 2)y, and the xy above and below the fraction is approximated, and the rest should be (2x) (y-x).

I don't know much about the third question, and I forgot what I learned before.

4.From the meaning of the title, it can be listed (root number x + root number y) 2=x+root number xy+y=(root number 5 + root number 3) 2=8+2 times root number 15, that is to say, x+root number xy+y=8+2 times root number 15, where root number xy = root number 15 - root number 3, and the value of x+y can be obtained by subtracting the two.

5.The root number 8, root number 18, and one-eighth of the root number are all solved in the form of x times the root number 2. I don't know if the "a+b root number 2" in the title refers to a+ (b root number 2) or (a+b) root number 2, in short, it should be calculated according to this method.

I don't guarantee that the above is correct.

But you can refer to it.