Question

3)So sánh

a)\(3\sqrt{11}\)và\(2\sqrt{15}\)

b)\(\dfrac{1}{4}\sqrt{5}\)và\(5\sqrt{\dfrac{1}{4}}\)

Answer 1

a)

\(3\sqrt{11}=\sqrt{9}.\sqrt{11}=\sqrt{99}\\ 2\sqrt{15}=\sqrt{4}.\sqrt{15}=\sqrt{90}\)

Vì \(\sqrt{99}>\sqrt{90}\)

\(\Rightarrow3\sqrt{11}>2\sqrt{15}\)

b)

\(\dfrac{1}{4}\sqrt{5}=\sqrt{\dfrac{1}{16}}.\sqrt{5}=\sqrt{\dfrac{5}{16}}\\ 5.\sqrt{\dfrac{1}{4}}=\sqrt{25}.\sqrt{\dfrac{1}{4}}=\sqrt{\dfrac{25}{4}}=\sqrt{\dfrac{100}{16}}\)

Vì \(\sqrt{\dfrac{5}{16}}< \sqrt{\dfrac{100}{16}}\)

\(\Rightarrow\dfrac{1}{4}\sqrt{5}< 5\sqrt{\dfrac{1}{4}}\)