Question

so sánh

d, 2\(\sqrt{3}\) +1 và 3\(\sqrt{2}\)

e,\(\sqrt{5}\)+3 và \(\sqrt{7}\)+1

f,\(\sqrt{5}+\sqrt{7}\)và 2\(\sqrt{6}\)

Answer 1

d: \(\left(2\sqrt{3}+1\right)^2=13+4\sqrt{3}\)

\(\left(3\sqrt{2}\right)^2=18=13+5\)

mà \(4\sqrt{3}>5\)

nên \(2\sqrt{3}+1>3\sqrt{2}\)

e: \(\left(3+\sqrt{5}\right)^2=14+6\sqrt{5}\)

\(\left(\sqrt{7}+1\right)^2=8+2\sqrt{7}\)

mà 14>8; \(6\sqrt{5}>2\sqrt{7}\)

nên \(3+\sqrt{5}>\sqrt{7}+1\)

f: \(\left(\sqrt{5}+\sqrt{7}\right)^2=12+2\sqrt{35}\)

\(\left(2\sqrt{6}\right)^2=24=12+12\)

mà \(2\sqrt{35}< 12\)

nên \(\sqrt{5}+\sqrt{7}< 2\sqrt{6}\)