15, original formula =(a/b)b? √(ab)×(-3a/2)√b×3√(a/b)

=ab√(ab)×(-9/2)a√a

=(-9a？ b/2)√(a？ b)

=-4.5a？ bìb

16, the original formula = [√ y (√ x-√ y)/(x-y)]-√ (xy)+[x √ y (√ x-√ y)]+√ (xy)

=[(√( xy)-y)/(x-y)]+[(x √( xy)-xy)/(x-y)]

=[( 1+x)√(xy)-xy-y]/(x-y)

17、a=√2

√2x-√2 & lt； 2√2

√2x & lt； 3√2

X< three

∴x= 1、2

18, ∫△BCD is an equilateral triangle, ∠ DBC = 60.

∴∠DBA=30

∴BD=2AD=2√2

AB=√6

∴ The circumference is 2×2√2+√2+√6=5√2+√6.

19, ① The original formula =1+(1/2)-[1/(2+√ 5)] = 3.5-√ 5.

②√{ 1+[ 1/(n- 1)？ ]+( 1/n？ )}

= 1+[ 1/(n- 1)]-[ 1/(n- 1+n)]

= 1+[ 1/(n- 1)]-[ 1/(2n- 1)]

=(2n？ -2n+ 1)/(2n？ -3n+ 1)

20. There are many methods: Examples are as follows:

① Arrange six squares into 1 row or 1 column to get a rectangle with length 12×6 and width 12.

The diagonal is √(72? + 12? )= 12√37cm

② Arrange six squares in two rows, three in each row, and get a rectangle with length 12×3 and width 12×3.

The diagonal is √(36? ×2)=36√2

1 1, the original formula = 8 √ 6-18 √ 6+12 √ 6-10 √ 6.

=-8√6

12, original formula =-(√2-√3)?

=2√6-5

13, original formula =6×( 1/2)÷5√2.

=3÷5√2

=(3/5)×(√2/2)

=0.3√2

14, the original formula = 2b× (1/b )×√ (AB)+3×√ (AB)-4a× (1/a) √ (AB)-3 √ (AB).

=2√(ab)+3√(ab)-4√(ab)-3√(ab)

=-2√(ab)