化簡以下實數

Way1 :

√2 (3－√ 18)

= 3 √2 - √ ( 2 x 18 )

= 3 √2 - √ 36

= 3 √2 - 6

= √18 - 6 <--- This is the ans . ( Or 3 ( √2 - 2 ) , √18 ( 1 - √2 ) is also OK , but I think 3 √2 - 6 is better . )

Way2 :

√2 (3－√18)

= √2 [ 3－√ ( 9 x 2 ) ]

= √2 [ 3 - ( √2 ) x ( √9 ) ]

= √2 [ 3 - ( √2 ) x 3 ]

= ( √2 ) ( 3 ) ( 1 - √2 )

= ( √2 ) ( √9 ) ( 1 - √2 )

= √18 ( 1 - √2 ) < --- ( You can stop but I will not . )

= √18 - ( √18 ) ( √2 )

= √18 - √36

= √18 - 6

Way1 : √2 (3－√ 18)
= 3 √2 - √ ( 2 x 18 )
= 3 √2 - √ 36
= 3 √2 - 6
=3(√2-2)
Way2 : √2 (3－√18)
= √2 [ 3－√ ( 9 x 2 ) ]
= √2 [ 3 - ( √2 ) x ( √9 ) ]
= √2 [ 3 - ( √2 ) x 3 ]
= ( √2 ) ( 3 ) ( 1 - √2 )
= ( √2 ) ( √9 ) ( 1 - √2 )
= √18 ( 1 - √2 ) < --- ( You can stop but I will not . )
= √18 - ( √18 ) ( √2 )
= √18 - √36
= √18 - 6 < --- ( You can stop but I will not . )
=3√2-6
=3(√2-2)

√2 (3－√18)
sqrt2(3-3sqrt2)
3sqrt2-3(sqrt2)^2
3sqrt2-6
3(sqrt2-2)


2010-10-05 17:53:53 補充：
I solved it full of steps...............

2010-10-05 17:54:53 補充：
To 林頌賢 :
√18 - 6 (it can further simplify!)

√2 (3－√18)
=3√2-√36
=3√2-6
=3(√2-1)

2010-10-05 17:54:05 補充：
唉~~~計得快得濟....錯咗
3(√2-2)先啱~~~