Thực hiện các phép tính sau:
a, \(\sqrt{\left(3+\sqrt{2}\right)^2}-\sqrt{\left(1-\sqrt{2}\right)^2}\)
b, \(\sqrt{\left(\sqrt{5}-\sqrt{2}\right)^2}+\sqrt{\left(\sqrt{5}+\sqrt{2}\right)^2}\)
c,\(\sqrt{\left(\sqrt{2}+1\right)^2}-\sqrt{\left(\sqrt{2}-5\right)^2}\)
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a) \(\sqrt{\left(3+\sqrt{2}\right)^2}-\sqrt{\left(1-\sqrt{2}\right)^2}\) \(=\left|3+\sqrt{2}\right|-\left|1-\sqrt{2}\right|\)
\(=\left(3+\sqrt{2}\right)-\left(\sqrt{2}-1\right)\) \(=3+\sqrt{2}-\sqrt{2}+1=4\)
b) \(\sqrt{\left(\sqrt{5}-\sqrt{2}\right)^2}+\sqrt{\left(\sqrt{5}+\sqrt{2}\right)^2}\) \(=\left|\sqrt{5}-\sqrt{2}\right|+\left|\sqrt{5}+\sqrt{2}\right|\)
\(=\left(\sqrt{5}-\sqrt{2}\right)+\left(\sqrt{5}+\sqrt{2}\right)\) \(=\sqrt{5}-\sqrt{2}+\sqrt{5}+\sqrt{2}=2\sqrt{5}\)
c) \(\sqrt{\left(\sqrt{2}+1\right)^2}-\sqrt{\left(\sqrt{2}-5\right)^2}\) \(=\left|\sqrt{2}+1\right|-\left|\sqrt{2}-5\right|\)
\(=\left(\sqrt{2}+1\right)-\left(5-\sqrt{2}\right)\) \(=\sqrt{2}+1-5+\sqrt{2}=2\sqrt{2}-4\)
