Question

Rút gọn:

a) \(\sqrt{\left(\sqrt{5}-\sqrt{2}\right)^2}-\sqrt{\left(\sqrt{5}+\sqrt{2}\right)^2}\).

b) \(\sqrt{\left(1-\sqrt{2}\right)^2}-\sqrt{\left(2-\sqrt{5}\right)^2}\).

c) \(\sqrt{46-6\sqrt{5}}-\sqrt{29-12\sqrt{5}}.\)

Answer 1

a, \(\sqrt{\left(\sqrt{5}-\sqrt{2}\right)^2}-\sqrt{\left(\sqrt{5}+\sqrt{2}\right)^2}\)

= \(\left|\text{√}5-\text{√}2\right|\)-\(\left|\text{√}5+\text{√}2\right|\)

= √5 -√2 - √5 - √2

= -2√2

b, \(\sqrt{\left(1-\sqrt{2}\right)^2}-\sqrt{\left(2-\sqrt{5}\right)^2}\)

= \(\left|1-\text{√}2\right|\) - \(\left|2-\text{√}5\right|\)

= √2 - 1 + 2 - √5

= √2-√5 +1

c, \(\sqrt{46-6\sqrt{5}}-\sqrt{29-12\sqrt{5}}\)

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

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

= 3√5 - 1 - 2√5 +3

= √5 + 2