Question

Rút gọn biểu thức:

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

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

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

Answer 1

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

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