Question

Tính giá trị của các biểu thức sau: √(3 - √5)² + √5 ;√3 - √(1+√3)² ; √(√3 - 1)² - √3

Answer 1

`\sqrt{(3-\sqrt{5})^2}+\sqrt{5}=|3-\sqrt{5}|+\sqrt{5}=3-\sqrt{5}+\sqrt{5}=3`

`\sqrt{3}-\sqrt{(1+\sqrt{3})^2}=\sqrt{3}-|1+\sqrt{3}|=\sqrt{3}-1-\sqrt{3}=-1`

`\sqrt{(\sqrt{3}-1)^2}-\sqrt{3}=|\sqrt{3}-1|-\sqrt{3}=\sqrt{3}-1-\sqrt{3}=-1`

Answer 2

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

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

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