化简根式……

（√27+√1/3)-(√12- √1/5+√45)
= √(9)(3) + √1/3 - √(3)(4) + √1/5 - √(9)(5)
= 3√3 + √1/3 - 2√3 + √1/5 - 3√5
= √3 + √1/3 + √1/5 - 3√5
= √3(1)(1 + 1/3) + √5(1/5 -3)
= √3(1)(4/3) + √5(1/5 -3)
= (4/3)√3 - (14/5)√5

≡≡≡≡≡≡≡≡≡≡≡≡≡≡≡≡≡≡≡≡

1/(3+2√2) * (3-2√2)/(3-2√2)
= (3-2√2)/[(3+2√2)(3-2√2)]
= (3-2√2)/[(3^2 + 3(2√2) - 3(2√2) -(2√2)^2]
= (3-2√2)/(9 - 8)
= 3 - 2√2

≡≡≡≡≡≡≡≡≡≡≡≡≡≡≡≡≡≡≡≡

(a-b)√5(a+s)/8(a-b)
= √5(a+s)/8

≡≡≡≡≡≡≡≡≡≡≡≡≡≡≡≡≡≡≡≡

a+b/a-b,a=1/√2 +1,b=1/√2 -1
= (1/√2) + (1/√2 -1)/(1/√2) - 1/√2 -1
= (1/√2 -1)(√2) - 1
= 1 - √2 -1
= √2