\(\text{a, Ta có:}\)

\(3\sqrt{7}=\sqrt{3^27}=\sqrt{63}\)

\(9=\sqrt{81}\)

\(\text{Vì}:\sqrt{81}>\sqrt{63}\Rightarrow3\sqrt{7}< 9\)

\(\text{b, Vì}\) \(-\sqrt{3}>-\sqrt{5}\Rightarrow-\sqrt{\sqrt{3}}>-\sqrt{\sqrt{5}}\)

\(c,\sqrt{51}-\sqrt{3}\approx5,4>5\)

\(d.\text{Vì}\) \(5>\sqrt{5}\Rightarrow\sqrt{85+5}>\sqrt{85+\sqrt{5}}\)

cvfbhm,

Xin lỗi em ko biết làm , em vẫn chưa lên lớp 9

1)\(\left(\frac{1}{a-\sqrt{a}}+\frac{1}{\sqrt{a}-1}\right):\frac{\sqrt{a}+1}{a-2\sqrt{a}+1}\)

\(=\left(\frac{1}{\sqrt{a}\left(\sqrt{a}-1\right)}+\frac{\sqrt{a}}{\sqrt{a}\left(\sqrt{a}-1\right)}\right)\cdot\frac{\left(\sqrt{a}-1\right)^2}{\sqrt{a}+1}\)

\(=\frac{\sqrt{a}+1}{\sqrt{a}\left(\sqrt{a}-1\right)}\cdot\frac{\left(\sqrt{a}-1\right)^2}{\sqrt{a}+1}\)

\(=\frac{\sqrt{a}-1}{\sqrt{a}}\)

\(\sqrt{5}-17\sqrt{3}\)

\(4\sqrt{12}-3\sqrt{45}-5\sqrt{75}+2\sqrt{125}\\ =8\sqrt{3}-9\sqrt{5}-25\sqrt{3}+10\sqrt{5}\\ \sqrt{5}-17\sqrt{3}\)

\(\sqrt{10}-\sqrt{\dfrac{5}{3}}-\sqrt{18}\)

\(=\sqrt{10}-\dfrac{\sqrt{5}}{\sqrt{3}}-3\sqrt{2}\)

\(=\sqrt{10}-\dfrac{\sqrt{15}}{3}-3\sqrt{2}\)

\(=\dfrac{3\sqrt{10}-\sqrt{15}-9\sqrt{2}}{3}\)

\(\sqrt{4}+\sqrt{15}-\sqrt{4}-\sqrt{15}-\sqrt{2}-\sqrt{3}\)

\(=-\sqrt{3}-\sqrt{2}\)