Question

Thực hiện phép tính (rút gọn biểu thức) 

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

b) \(\sqrt{\left(\sqrt{7}-2\sqrt{2}\right)^2}\)-\(\sqrt{\left(\sqrt{7}+2\sqrt{2}\right)^2}\)

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

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

Answer 1

Lời giải:

a. $=|3+\sqrt{2}|-|3-2\sqrt{2}|=(3+\sqrt{2})-(3-2\sqrt{2})$

$=3\sqrt{2}$

b. $=|\sqrt{7}-2\sqrt{2}|-|\sqrt{7}+2\sqrt{2}|$

$=(2\sqrt{2}-\sqrt{7})-(\sqrt{7}+2\sqrt{2})$

$=-2\sqrt{7}$

c.

$=|3+\sqrt{5}|+|3-\sqrt{5}|=(3+\sqrt{5})+(3-\sqrt{5})=6$

d.

$=|2-\sqrt{3}|-|2+\sqrt{3}|=(2-\sqrt{3})-(2+\sqrt{3})=-2\sqrt{3}$