a)
\(\sqrt{4-2\sqrt{3}}-\sqrt{3}\)
\(=\sqrt{\left(\sqrt{3}-1\right)^2}-\sqrt{3}\)
\(=-1\)
b)
\(\sqrt{11+6\sqrt{2}}-3+\sqrt{2}\)
\(=\sqrt{\left(3+\sqrt{2}\right)^2}-3+\sqrt{2}\)
\(=2\sqrt{2}\)
c)
\(\sqrt{10+2\sqrt{9}}-\sqrt{9}\)
\(=\sqrt{\left(\sqrt{9}+1\right)^2}-\sqrt{9}\)
\(=1\)
a) \(\sqrt{4-2\sqrt{3}}-\sqrt{3}\)
= \(\sqrt{3-2\sqrt{3}+1}-\sqrt{3}\)
= \(\sqrt{\left(\sqrt{3}\right)^2-2.\sqrt{3}.1+1}-\sqrt{3}\)
= \(\sqrt{\left(\sqrt{3}-1\right)^2}-\sqrt{3}\)
= \(\left|\sqrt{3}-1\right|-\sqrt{3}=\sqrt{3}-1-\sqrt{3}\) = -1
b) \(\sqrt{11+6\sqrt{2}}-3+\sqrt{2}\)
= \(\sqrt{2+6\sqrt{2}+9}-3+\sqrt{2}\)
= \(\sqrt{\left(\sqrt{2}+3\right)^2}-3+\sqrt{2}\)
= \(\left|\sqrt{2}+3\right|-3+\sqrt{2}\)
= \(\sqrt{2}+3-3+\sqrt{2}=2\sqrt{2}\)
c) \(\sqrt{10+2\sqrt{9}}-\sqrt{9}=\sqrt{9+2\sqrt{9}+1}-\sqrt{9}=\sqrt{\left(\sqrt{9}+1\right)^2}-\sqrt{9}=\left|\sqrt{9}+1\right|-\sqrt{9}=\sqrt{9}+1-\sqrt{9}=1\)
