Question

giúp mình câu e,f

Answer 1

e: \(E=\sqrt{2+\sqrt{3}}\cdot\sqrt{2+\sqrt{2+\sqrt{3}}}\cdot\sqrt{2-\sqrt{2+\sqrt{3}}}\)

\(=\sqrt{2+\sqrt{3}}\cdot\sqrt{4-\left(2+\sqrt{3}\right)}\)

\(=\sqrt{2+\sqrt{3}}\cdot\sqrt{2-\sqrt{3}}=\sqrt{4-3}=1\)

f: \(F=\sqrt{\left(1-\sqrt{2024}\right)^2}\cdot\sqrt{2025+2\sqrt{2024}}\)

\(=\sqrt{\left(\sqrt{2024}-1\right)^2}\cdot\sqrt{\left(\sqrt[]{2024}+1\right)^2}\)

\(=\left(\sqrt{2024}-1\right)\left(\sqrt{2024}+1\right)\)

=2024-1

=2023