Question

Answer 1

\(\sqrt{\left(\sqrt{5}-3\right)^2}+\sqrt{\left(2-\sqrt{5}\right)^2}-1\)

\(=\left|\sqrt{5}-3\right|+\left|2-\sqrt{5}\right|-1\)

\(=3-\sqrt{5}+\sqrt{5}-2-1\)(vì \(\sqrt{5}< 3;\sqrt{5}>2\))

=0

Answer 2

Vì $ 5 < 9 ⇔ \sqrt{5} < \sqrt{9} ⇔ \sqrt{5} < 3 ⇔ \sqrt{5} - 3 < 0$

Vì $ 4 < 5 ⇔ \sqrt{4} < \sqrt{5} ⇔ 2 < \sqrt{5} ⇔ 2 - \sqrt{5} < 0$

Ta có : 

$\sqrt{ ( \sqrt{5} -3)^2} + \sqrt{ ( 2- \sqrt{5})^2} - 1$
$= -( \sqrt{5} - 3) - (2 - \sqrt{5}) - 1$
$= 3 - \sqrt{5} + \sqrt{5} - 2 - 1$

$= 0$