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HT.Phong (9A5)
4 tháng 9 2023 lúc 11:36

b) \(B=\sqrt{6+2\sqrt{5-\sqrt{13+\sqrt{48}}}}\)

\(B=\sqrt{6+2\sqrt{5-\sqrt{13+4\sqrt{3}}}}\)

\(B=\sqrt{6+2\sqrt{5-\sqrt{\left(2\sqrt{3}\right)^2+2\cdot2\sqrt{3}\cdot1+1^2}}}\)

\(B=\sqrt{6+2\sqrt{5-\sqrt{\left(2\sqrt{3}+1\right)^2}}}\)

\(B=\sqrt{6+2\sqrt{5-2\sqrt{3}-1}}\)

\(B=\sqrt{6+2\sqrt{4-2\sqrt{3}}}\)

\(B=\sqrt{6+2\sqrt{\left(\sqrt{3}\right)^2-2\cdot\sqrt{3}\cdot1+1^2}}\)

\(B=\sqrt{6+2\sqrt{\left(\sqrt{3}-1\right)^2}}\)

\(B=\sqrt{6+2\left|\sqrt{3}-1\right|}\)

\(B=\sqrt{6+2\sqrt{3}-2}\)

\(B=\sqrt{4+2\sqrt{3}}\)

\(B=\sqrt{\left(\sqrt{3}\right)^2+2\cdot\sqrt{3}\cdot1+1^2}\)

\(B=\sqrt{\left(\sqrt{3}+1\right)^2}\)

\(B=\sqrt{3}+1\)

HT.Phong (9A5)
4 tháng 9 2023 lúc 11:40

a) \(A=\sqrt{\sqrt{5}-\sqrt{3-\sqrt{29-6\sqrt{20}}}}\)

\(A=\sqrt{\sqrt{5}-\sqrt{3-\sqrt{29-12\sqrt{5}}}}\)

\(A=\sqrt{\sqrt{5}-\sqrt{3-\sqrt{\left(2\sqrt{5}\right)^2-2\cdot3\cdot2\sqrt{5}+3^2}}}\)

\(A=\sqrt{\sqrt{5}-\sqrt{3-\sqrt{\left(2\sqrt{5}-3\right)^2}}}\)

\(A=\sqrt{\sqrt{5}-\sqrt{3-\left|2\sqrt{5}-3\right|}}\)

\(A=\sqrt{\sqrt{5}-\sqrt{3-2\sqrt{5}+3}}\)

\(A=\sqrt{\sqrt{5}-\sqrt{6-2\sqrt{5}}}\)

\(A=\sqrt{\sqrt{5}-\sqrt{\left(\sqrt{5}\right)^2-2\cdot\sqrt{5}\cdot1+1^2}}\)

\(A=\sqrt{\sqrt{5}-\sqrt{\left(\sqrt{5}-1\right)^2}}\)

\(A=\sqrt{\sqrt{5}-\left|\sqrt{5}-1\right|}\)

\(A=\sqrt{\sqrt{5}-\sqrt{5}+1}\)

\(A=\sqrt{1}\)

\(A=1\)

Nguyễn Lê Phước Thịnh
4 tháng 9 2023 lúc 11:42

c: \(C=\sqrt{4+\sqrt{5\sqrt{3}+5\sqrt{48-10\sqrt{7+4\sqrt{3}}}}}\)

\(C=\sqrt{4+\sqrt{5\sqrt{3}+5\sqrt{48-10\sqrt{\left(2+\sqrt{3}\right)^2}}}}\)

\(C=\sqrt{4+\sqrt{5\sqrt{3}+5\sqrt{48-10\left(2+\sqrt{3}\right)}}}\)

\(C=\sqrt{4+\sqrt{5\sqrt{3}+5\sqrt{28-10\sqrt{3}}}}\)

\(C=\sqrt{4+\sqrt{5\sqrt{3}+5\left(5-\sqrt{3}\right)}}\)

\(=\sqrt{4+\sqrt{25}}=\sqrt{4+5}=3\)

Toru
4 tháng 9 2023 lúc 11:56

\(a,A=\sqrt{\sqrt{5}-\sqrt{3-\sqrt{29-6\sqrt{20}}}}\)

\(=\sqrt{\sqrt{5}-\sqrt{3-\sqrt{\left(\sqrt{20}\right)^2-2\cdot\sqrt{20}\cdot3+3^2}}}\)

\(=\sqrt{\sqrt{5}-\sqrt{3-\sqrt{\left(\sqrt{20}-3\right)^2}}}\)

\(=\sqrt{\sqrt{5}-\sqrt{3-\left|\sqrt{20}-3\right|}}\)

\(=\sqrt{\sqrt{5}-\sqrt{3-\sqrt{20}+3}}\)

\(=\sqrt{\sqrt{5}-\sqrt{6-2\sqrt{5}}}\)

\(=\sqrt{\sqrt{5}-\sqrt{\left(\sqrt{5}\right)^2-2\sqrt{5}+1}}\)

\(=\sqrt{\sqrt{5}-\sqrt{\left(\sqrt{5}-1\right)^2}}\)

\(=\sqrt{\sqrt{5}-\left|\sqrt{5}-1\right|}\)

\(=\sqrt{\sqrt{5}-\sqrt{5}+1}\)

\(=1\)

\(b,B=\sqrt{6+2\sqrt{5-\sqrt{13+\sqrt{48}}}}\)

\(=\sqrt{6+2\sqrt{5-\sqrt{\left(\sqrt{12}\right)^2+2\sqrt{12}+1}}}\)

\(=\sqrt{6+2\sqrt{5-\sqrt{\left(\sqrt{12}+1\right)^2}}}\)

\(=\sqrt{6+2\sqrt{5-\left|\sqrt{12}+1\right|}}\)

\(=\sqrt{6+2\sqrt{5-\sqrt{12}-1}}\)

\(=\sqrt{6+2\sqrt{4-\sqrt{12}}}\)

\(=\sqrt{6+2\sqrt{\left(\sqrt{3}\right)^2-2\sqrt{3}+1}}\)

\(=\sqrt{6+2\sqrt{\left(\sqrt{3}-1\right)^2}}\)

\(=\sqrt{6+2\left|\sqrt{3}-1\right|}\)

\(=\sqrt{6+2\sqrt{3}-2}\)

\(=\sqrt{4+2\sqrt{3}}\)

\(=\sqrt{\left(\sqrt{3}\right)^2+2\sqrt{3}+1}\)

\(=\sqrt{\left(\sqrt{3}+1\right)^2}\)

\(=\left|\sqrt{3}+1\right|\)

\(=\sqrt{3}+1\)

\(c,C=\sqrt{4+\sqrt{5\sqrt{3}+5\sqrt{48-10\sqrt{7+4\sqrt{3}}}}}\)

\(=\sqrt{4+\sqrt{5\sqrt{3}+5\sqrt{48-10\sqrt{\left(\sqrt{3}\right)^2+2\cdot\sqrt{3}\cdot2+2^2}}}}\)

\(=\sqrt{4+\sqrt{5\sqrt{3}+5\sqrt{48-10\sqrt{\left(\sqrt{3}+2\right)^2}}}}\)

\(=\sqrt{4+\sqrt{5\sqrt{3}+5\sqrt{48-10\left|\sqrt{3}+2\right|}}}\)

\(=\sqrt{4+\sqrt{5\sqrt{3}+5\sqrt{48-10\sqrt{3}-20}}}\)

\(=\sqrt{4+\sqrt{5\sqrt{3}+5\sqrt{28-10\sqrt{3}}}}\)

\(=\sqrt{4+\sqrt{5\sqrt{3}+5\sqrt{5^2-2\cdot5\cdot\sqrt{3}+\left(\sqrt{3}\right)^2}}}\)

\(=\sqrt{4+\sqrt{5\sqrt{3}+5\sqrt{\left(5-\sqrt{3}\right)^2}}}\)

\(=\sqrt{4+\sqrt{5\sqrt{3}+5\left|5-\sqrt{3}\right|}}\)

\(=\sqrt{4+\sqrt{5\sqrt{3}+25-5\sqrt{3}}}\)

\(=\sqrt{4+\sqrt{25}}\)

\(=\sqrt{4+5}\)

\(=\sqrt{9}\)

\(=3\)

#Urushi


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