Câu 4: Trang 33 sách VNEN 9 tập 1Thực hiện phép tính:a)$\left ( \sqrt{\frac{9}{2}} +...

a)
$\left ( \sqrt{\frac{9}{2}} + \sqrt{\frac{1}{2}} - \sqrt{2} \right )$.$\sqrt{2}$= $\left ( \frac{\sqrt{9}}{\sqrt{2}}+ \frac{\sqrt{1}}{\sqrt{2}} - \sqrt{2} \right )$.$\sqrt{2}$
= 3 + 1 - 2
= 2

b)
($\sqrt{3}$ - $\sqrt{2}$ + 1)($\sqrt{3}$ - 1)= ($\sqrt{3}$ + 1 - $\sqrt{2}$)($\sqrt{3}$ - 1)
= ($\sqrt{3}$ + 1)($\sqrt{3}$ - 1) - $\sqrt{2}$($\sqrt{3}$ - 1)
= 3 - 1 - $\sqrt{6}$ + $\sqrt{2}$
= 2 - $\sqrt{6}$ + $\sqrt{2}$

c)
$(\sqrt{2} + \sqrt{5})^{2}$ = $(\sqrt{2})^{2}$ + $(\sqrt{5})^{2}$ + 2$\sqrt{2}$$\sqrt{5}$
= 2 + 5 + 2$\sqrt{2}$$\sqrt{5}$
= 7 + 2$\sqrt{10}$

d)
($\sqrt{8}$ - 5$\sqrt{2}$ + $\sqrt{20}$).$\sqrt{5}$ - $\left ( 3\sqrt{\frac{1}{10}} + 10 \right )$= (2$\sqrt{2}$ - 5$\sqrt{2}$ + 2$\sqrt{5}$).$\sqrt{5}$ - $\left ( 3\frac{\sqrt{10}}{10} + 10 \right )$
= (- 3$\sqrt{2}$ + 2$\sqrt{5}$).$\sqrt{5}$ - $\left ( 3\sqrt{\frac{1}{10}} + 10 \right )$
= - 3$\sqrt{10}$ + 10 - 3$\sqrt{\frac{\sqrt{10}}{10}}$ - 10
= - 33$\frac{\sqrt{10}}{10}$

Vậy các kết quả là:
a) 2
b) 2 - $\sqrt{6}$ + $\sqrt{2}$
c) 7 + 2$\sqrt{10}$
d) -33$\frac{\sqrt{10}}{10}$