Question

Rút gọn
a, \(\sqrt{4+\sqrt{7+4\sqrt{3}}}\)

b, \(\sqrt{5+\sqrt{3}+5\sqrt{48-10\sqrt{7+4\sqrt{3}}}}\)

c, \(\sqrt{13+30\sqrt{2+\sqrt{9+4\sqrt{2}}}}\)

d, \(\sqrt{x+2\sqrt{x}-1}\)+ \(\sqrt{x-2\sqrt{x-1}}\) ( x \(\ge\)0)

Answer 1

a: \(=\sqrt{4+2+\sqrt{3}}=\sqrt{6+\sqrt{3}}\)

c: \(=\sqrt{13+30\sqrt{2+2\sqrt{2}+1}}\)

\(=\sqrt{13+30\left(\sqrt{2}+1\right)}\)

\(=\sqrt{43+30\sqrt{2}}\)

d: \(\sqrt{x+2\sqrt{x-1}}+\sqrt{x-2\sqrt{x-1}}\)

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

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

TH1: x>=2

\(D=\sqrt{x-1}+1+\sqrt{x-1}-1=2\sqrt{x-1}\)

TH2: 0<=x<2

\(D=\sqrt{x-1}+1+1-\sqrt{x-1}=2\)