Question

计算与化简

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1.(1/2√28-3/2√84)×√14 2.√一又三分一÷√二又三分二×√一又五分三
3.3√48-9√1/3+3√12 4.（√48+√20）+（√12-√5）
5.√2×√6/√3-1 6.√（√3+1）（√3-1）
7.√72-4√1/2-1/7√98+√一又1/8 8.√9a+a/3√1/a+1/2a√a^3
9.(2+√3^2008)(2-√3)^2006 10.（√3a-3√27a^3)÷√a/3

Answer 1

1.(1/2√28-3/2√84)×√14
=(√7-3√21)×√14
=√7(1-3√3)×√7×√2
= 7√2(1-3√3)
=7√2-21√6

2.√一又三分一÷√二又三分二×√一又五分三
=√(4/3)÷√(8/3)×√(8/5)
=√(4/3)÷[√(4/3)×√2]×√(8/5)
=1÷√2×√(8/5)
=√2/2×2√(2/5)
=√2×√(2/5)
=√2×√10/5
=√20/5
=2√5/5

3.3√48-9√1/3+3√12
=12√3-3√3+6√3
=15√3

4.（√48+√20）+（√12-√5）
=4√3+2√5+2√3-√5
=6√3+√5

5.√2×√6/(√3-1)
=2√3/(√3-1)
=2√3(√3+1)/[(√3-1)(√3+1)
=2√3(√3+1)/2
=√3(√3+1)
=3+√3

6.√（√3+1）（√3-1）
=3-1
=2

7.√72-4√1/2-1/7√98+√一又1/8
=6√2-2√2-√2+√(9/8)
=3√2+3√(1/2)/2
=3√2+3√2/4
=15√2/4

8.√9a+a/3√1/a+1/2a√a^3
=3√a+√a/3+√a/2
=18√a/6+2√a/6+3√a/6
=23√a/6

9.(2+√3)^2008(2-√3)^2006
=(2+√3)^2*(2+√3)^2006*(2-√3)^2006
=(2+√3)^2*[(2+√3)(2-√3)]^2006
=(2+√3)^2*1^2006
=(2+√3)^2
=7+4√3

10.（√3a-3√27a^3)÷√(a/3)
=（√3a-9a√3a)÷√(a/3)
=√3a(1-9a)÷√(3a)/3
=(1-9a)÷1/3
= (1-9a)*3
=3-27a