Giải câu 6 trang 23 toán VNEN 9 tập 1

a) $\frac{1}{7}$$\sqrt{51}$ < $\frac{1}{7}$$\sqrt{64}$ = $\frac{8}{7}$

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

=> $\frac{1}{7}$$\sqrt{51}$ < $\frac{1}{9}$$\sqrt{150}$ 

b) $\sqrt{2017}$ - $\sqrt{2016}$ = $\frac{(\sqrt{2017}-\sqrt{2016})(\sqrt{2017}+\sqrt{2016})}{\sqrt{2017}+\sqrt{2016}}=\frac{1}{\sqrt{2017}+\sqrt{2016}}$

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

Vì $\sqrt{2017}+\sqrt{2016}$ > $\sqrt{2016}+\sqrt{2015}$ => $\frac{1}{\sqrt{2017}+\sqrt{2016}}$ < $\frac{1}{\sqrt{2016}+\sqrt{2015}}$

=> $\sqrt{2017}$ - $\sqrt{2016}$ < $\sqrt{2016}$ - $\sqrt{2015}$