Question

[•๖ۣۜ长υɀ༄]

So sánh (không dùng máy tính bỏ túi):

\(a,\sqrt{2019.2021}\)và \(2020\)

\(b,\sqrt{2}+\sqrt{3}\)và \(3\)

\(c,9+4\sqrt{5}\)và \(16\)

\(d,\sqrt{11}-\sqrt{3}\)và \(2\)

Answer 1

[12345678901]

a, 2020 lớn hơn

Answer 2

[Edogawa Conan]

a)\(\left(\sqrt{2019.2021}\right)^2=2019.2021=\left(2020-1\right)\left(2020+1\right)=2020^2-1< 2020^2\)

=> \(\sqrt{2019.2021}< 2020\)

b) \(\left(\sqrt{2}+\sqrt{3}\right)^2=5+2\sqrt{6}>5+2\sqrt{4}=5+2.2=9\)

=> \(\sqrt{2}+\sqrt{3}>3\)

c) \(9+4\sqrt{5}=4+4\sqrt{5}+5=\left(2+\sqrt{5}\right)^2>\left(2+\sqrt{4}\right)^2=\left(2+2\right)^2=16\)

=> \(9+4\sqrt{5}>16\)

d) \(\sqrt{11}-\sqrt{3}>\sqrt{9}-\sqrt{1}=3-1=2\)

=> \(\sqrt{11}-\sqrt{3}>2\)