平方根(2) 送10分

1.
(3√2-√6)2
= (3√2)2 - 2(3√2)( √6) + (√6)2
= 18 - 6√12 + 6
= 18 - 6(2√3) + 6
= 24 - 12√3


2.
3√5(2√3 + 1)2
= 3√5[(2√3)2 + 2(2√3)(1) + (1)2]
= 3√5[12 + 4√3 + 1]
= 3√5[13 + 4√3]
= 3√5(13) + 3√5(4√3)
= 39√5 + 12√15


3.
√10(√5 - √2)2
= √10[(√5)2 - 2(√5)( √2) + (√2)2]
= √10[5 - 2√10 + 2]
= √10[7 - 2√10]
= √10(7) - √10(2√10)
= 7√10 - 20
= -20 + 7√10


4.
√6(3 + 2√2)2
= √6[(3)2 + 2(3)(2√2) + (2√2)2]
= √6[9 + 12√2 + 8]
= √6[17 + 12√2]
= √6(17) + √6(12√2)
= 17√6 + 12√12
= 17√6 + 12(2√3)
= 17√6 + 24√3


5.
(√3 - √5)2 + (√3 + √5)2
= [(√3)2 - 2(√3)(√5) + (√5)2] + [(√3)2 + 2(√3)(√5) + (√5)2]
= [3- 2√15 + 5] + [3 + 2√15 + 5]
= [8 - 2√15] + [8 + 2√15]
= 16


6.
(3√2 + 2√5)2 + (3√2 - 2√5)2
= [(3√2)2 + 2(3√2)(2√5) + (2√5)2] + [(3√2)2 - 2(3√2)(2√5) + (2√5)2]
= [18 + 12√10 + 20] + [18 - 12√10 + 20]
= [38 + 12√10] + [38 - 12√10]
= 76


7.
(1 + √2)(1 + √2 - √3)
= (1)(1 + √2 - √3) + √2(1 + √2 - √3)
= (1 + √2 + √3) + (√2 + 2 + √6)
= 1 + √2 + √3 + √2 + 2 + √6
= 3 + 2√2 + √3 + √6


8.
(√2 + √3)(√2 - √3 + 1)
= √2(√2 - √3 + 1) + √3(√2 - √3 + 1)
= 2 - √6 + √2 + √6 - 3 + √3
= -1 + √2 + √3


9.
(2√10 - 3√5)2
= (2√10)2 - 2(2√10)(3√5) + (3√5)2
= 40 - 12√50 + 45
= 85 - 12(5√2)
= 85 - 60√2


10.
(3√2 + 1)(5√2 + 2)
= 3√2(5√2 + 2) + 1(5√2 + 2)
= 30 + 6√2 + 5√2 + 2
= 32 + 11√2
=