Thực hiện phép tính
a)\(\sqrt{\left(\sqrt{2}-1\right)^2}+\sqrt{\left(3\sqrt{2}-2\right)^2}\)
b)\(2.\sqrt{\left(\sqrt{3}-1\right)^2}-\sqrt{\left(2\sqrt{3}+1\right)^2}\)
c)\(4.\sqrt{\left(2-\dfrac{\sqrt{3}}{2}\right)^2}-3.\sqrt{\left(\sqrt{3}-1\right)^2}\)
d)\(\sqrt{3+2\sqrt{2}}+\sqrt{3-2\sqrt{2}}\)
e)\(\left(\sqrt{3}-1\right)^2+\left(2\sqrt{3}+1\right)^2\)
g)\(\left(1-2\sqrt{2}\right)^2-\left(\sqrt{2}+1\right)^2\)
a, \(\sqrt{\left(\sqrt{2}-1\right)^2}+\sqrt{\left(3\sqrt{2}-2\right)^2}\)
\(=\left|\sqrt{2}-1\right|+\left|3\sqrt{2}-2\right|\)
\(=\sqrt{2}-1+3\sqrt{2}-2=4\sqrt{2}-3\)
b, \(2\sqrt{\left(\sqrt{3}-1\right)^2}-\sqrt{\left(2\sqrt{3}+1\right)^2}\)
\(=2\left|\sqrt{3}-1\right|-\left|2\sqrt{3}+1\right|\)
\(=2\sqrt{3}-2-2\sqrt{3}-1=-3\)
c, \(4\sqrt{\left(2-\dfrac{\sqrt{3}}{2}\right)^2}-3\sqrt{\left(\sqrt{3}-1\right)^2}\)
\(=4\left|2-\dfrac{\sqrt{3}}{2}\right|-3\left|\sqrt{3}-1\right|\)
\(=8-2\sqrt{3}-3\sqrt{3}+3=11-5\sqrt{3}\)
d, \(\sqrt{3+2\sqrt{2}}+\sqrt{3-2\sqrt{2}}\)
\(=\sqrt{\left(\sqrt{2}+1\right)^2}+\sqrt{\left(\sqrt{2}-1\right)^2}\)
\(=\left|\sqrt{2}+1\right|+\left|\sqrt{2}-1\right|\)
\(=\sqrt{2}+1+\sqrt{2}-1=2\sqrt{2}\)
a: Ta có: \(\sqrt{\left(\sqrt{2}-1\right)^2}+\sqrt{\left(3\sqrt{2}-2\right)^2}\)
\(=\sqrt{2}-1+3\sqrt{2}-2\)
\(=4\sqrt{2}-3\)
b: Ta có: \(2\cdot\sqrt{\left(\sqrt{3}-1\right)^2}-\sqrt{\left(2\sqrt{3}+1\right)^2}\)
\(=2\sqrt{3}-2-2\sqrt{3}-1\)
=-3
c: Ta có: \(4\cdot\sqrt{\left(2-\dfrac{\sqrt{3}}{2}\right)^2}-3\cdot\sqrt{\left(\sqrt{3}-1\right)^2}\)
\(=8-2\sqrt{3}-3\sqrt{3}+3\)
\(=11-5\sqrt{3}\)
d: Ta có: \(\sqrt{3+2\sqrt{2}}+\sqrt{3-2\sqrt{2}}\)
\(=\sqrt{2}+1+\sqrt{2}-1\)
\(=2\sqrt{2}\)
e: Ta có: \(\left(\sqrt{3}-1\right)^2+\left(2\sqrt{3}+1\right)^2\)
\(=4-2\sqrt{3}+13+4\sqrt{3}\)
\(=17+2\sqrt{3}\)
e, \(\left(\sqrt{3}-1\right)^2+\left(2\sqrt{3}+1\right)^2\)
\(=4-2\sqrt{3}+13+4\sqrt{3}\)
\(=17+2\sqrt{3}\)
g, \(\left(1-2\sqrt{2}\right)^2-\left(\sqrt{2}+1\right)^2\)
\(=9-4\sqrt{2}-3-2\sqrt{2}\)
\(=6-6\sqrt{2}\)
