Question

So sánh ( ko dung bảng số, máy tính )

a) \(\dfrac{1}{7}\sqrt{51}\) vs \(\dfrac{1}{9}\sqrt{150}\)

b) \(\sqrt{2017}-\sqrt{2016}\) vs \(\sqrt{2016}-\sqrt{2015}\)

Answer 1

Lời giải:

a)

Ta có: \(\frac{1}{7}\sqrt{51}< \frac{1}{7}\sqrt{64}=\frac{8}{7}\)

\(\frac{1}{9}\sqrt{150}> \frac{1}{9}\sqrt{144}=\frac{12}{9}=\frac{4}{3}=\frac{8}{6}> \frac{8}{7}\)

Do đó: \(\frac{1}{7}\sqrt{51}< \frac{1}{9}\sqrt{150}\)

b)

\(\sqrt{2017}-\sqrt{2016}=\frac{2017-2016}{\sqrt{2017}+\sqrt{2016}}=\frac{1}{\sqrt{2017}+\sqrt{2016}}< \frac{1}{\sqrt{2016}+\sqrt{2015}}\)

\(\sqrt{2016}-\sqrt{2015}=\frac{2016-2015}{\sqrt{2016}+\sqrt{2015}}=\frac{1}{\sqrt{2016}+\sqrt{2015}}\)

Do đó:

\(\sqrt{2017}-\sqrt{2016}< \sqrt{2016}-\sqrt{2015}\)