Question

so sánh

Answer 1

16 = 9 + 7 = 9 + √49

9 + 4√5 = 9 + √80

Do 49 < 80 nên √49 < √80

⇒ 9 + √49 < 9 + √80

Vậy 16 < 9 + 4√5

Answer 2

Ta có:

\(16=9+5=9+\sqrt{25}\)

\(9+4\sqrt{5}=9+\sqrt{4^2\cdot5}=9+\sqrt{20}\)

Mà: \(20< 25\)

\(\Rightarrow\sqrt{20}< \sqrt{25}\)

\(\Rightarrow9+\sqrt{20}< 9+\sqrt{25}\)

\(\Rightarrow9+4\sqrt{5}< 16\)

Answer 3

Giả sử \(16< 9+4\sqrt[]{5}\)

\(\Leftrightarrow7< 4\sqrt[]{5}\)

\(\Leftrightarrow7^2< \left(4\sqrt[]{5}\right)^2\)

\(\Leftrightarrow49< 80\left(luôn.đúng\right)\)

Vậy \(16< 9+4\sqrt[]{5}\)