Question

b)√(√2 +5)²-√2

c)√4-2√3  -2/√3 -1  +√3 -3/√3 -1

 

Answer 1

b: \(\sqrt{\left(\sqrt{2}+5\right)^2}-\sqrt{2}\)

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

\(=5+\sqrt{2}-\sqrt{2}=5\)

c: \(\sqrt{4-2\sqrt{3}}-\dfrac{2}{\sqrt{3}-1}+\dfrac{\sqrt{3}-3}{\sqrt{3}-1}\)

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

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

\(=\sqrt{3}-1-2\sqrt{3}-1=-\sqrt{3}-2\)