Question

Answer 1

a) \(\sqrt{\left(4+\sqrt{2}\right)^2}=\left|4+\sqrt{2}\right|=4+\sqrt{2}\)

b) \(\sqrt{\left(4-\sqrt{17}\right)^2}=\left|4-\sqrt{17}\right|=\sqrt{17}-4\)

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

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

Answer 2

a. 4 + \(\sqrt{2}\)

b. \(3-\sqrt{3}\)

c. \(4-\sqrt{17}\)

d. \(2\sqrt{3}+2-\sqrt{3}=\sqrt{3}+2\)