Question

Rút gọn

a,\(\sqrt{14+4\sqrt{3}.\sqrt{2}}\)

b,\(\sqrt{11-4\sqrt{3}.\sqrt{2}}\)

c,\(\sqrt{28+16\sqrt{3}}\)

d,\(\sqrt{11+4\sqrt{7}}\)

e,\(\sqrt{29-4\sqrt{7}}\)

f,\(\sqrt{21+6\sqrt{2}.\sqrt{3}}\)

Answer 1

\(a.\sqrt{14+4\sqrt{3}.\sqrt{2}}=\sqrt{12+2.2\sqrt{3}.\sqrt{2}+2}=2\sqrt{3}+\sqrt{2}\)

\(b.\sqrt{11-4\sqrt{3}.\sqrt{2}}=\sqrt{8-2.2\sqrt{2}.\sqrt{3}+3}=2\sqrt{2}-\sqrt{3}\)

\(c.\sqrt{28+16\sqrt{3}}=\sqrt{16+2.2\sqrt{3}.4+12}=4+2\sqrt{3}\)

\(d.\sqrt{11+4\sqrt{7}}=\sqrt{7+2.2\sqrt{7}+4}=\sqrt{7}+2\)

\(e.\sqrt{29-4\sqrt{7}}=\sqrt{28-2.2\sqrt{7}+1}=2\sqrt{7}-1\)

\(f.\sqrt{21+6\sqrt{2}.\sqrt{3}}=\sqrt{18+2.3\sqrt{2}.\sqrt{3}+3}=3\sqrt{2}+\sqrt{3}\)