Question

\(\sqrt{24+16\sqrt{2}}-\sqrt{24-16\sqrt{2}}\)

Answer 1

\(\sqrt{24+16\sqrt{2}}-\sqrt{24-16\sqrt{2}}\)

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

\(=4+2\sqrt{2}-4+2\sqrt{2}\)

\(=4\sqrt{2}\)

Answer 2

Giải:

\(\sqrt{24+16\sqrt{2}}-\sqrt{24-16\sqrt{2}}\)

\(=\sqrt{8+2.4.2\sqrt{2}+16}-\sqrt{16-2.4.2\sqrt{2}+8}\)

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

\(=2\sqrt{2}+4-\left(4-2\sqrt{2}\right)\)

\(=2\sqrt{2}+4-4+2\sqrt{2}\)

\(=4\sqrt{2}\)

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