Question

Rút gọn các biểu thức sau:

a) \(\sqrt{\left(\sqrt{3}-\sqrt{2}\right)^2}+\sqrt{\left(1-\sqrt{2}\right)^2}\);                  b) \(\sqrt{\left(\sqrt{7}-3\right)^2}+\sqrt{\left(\sqrt{7}+3\right)^2}\)

Answer 1

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

b) \(\sqrt {{{\left( {\sqrt 7  - 3} \right)}^2}}  + \sqrt {{{\left( {\sqrt 7  + 3} \right)}^2}} \)\( = \left| {\sqrt 7  - 3} \right| + \left| {\sqrt 7  + 3} \right|\)\( = 3 - \sqrt 7  + \sqrt 7  + 3\)\( = 6\)