Question

1.Rút gọn rồi tính:

a) \(\sqrt{117,5^2-26,5^2-1440}\)

b) \(\sqrt{146,5^2-109,5^2+27\times256}\)

2. So sánh:

\(\sqrt{2003}+\sqrt{2005}\)và  \(2\sqrt{2004}\)

Answer 1

2)

​\(\left(\sqrt{2003}+\sqrt{2005}\right)^2=2003+2005+2\sqrt{2003\times2005}\)

\(=4008+2\sqrt{\left(2004-1\right)\left(2004+1\right)}=4008+2\sqrt{2004^2-1}\)

\(\left(\sqrt{2004}+\sqrt{2004}\right)^2=2004+2004+2\sqrt{2004\times2004}\)

\(=4008+2\sqrt{2004^2}\)

Ta có \(2004^2>2004^2-1\Rightarrow\sqrt{2004^2}>\sqrt{2004^2-1}\Rightarrow4008+2\sqrt{2004^2}>4008+2\sqrt{2004^2-1}\)

Vậy \(2\sqrt{2004}>\sqrt{2003}+\sqrt{2005}\)

Answer 2

1.  a) 108
     b) 128
2.  >

Answer 3

cái mình cần là cách giải bạn ạ