Question

Rút gọn các biểu thức sau:

a) \(\dfrac{3-2\sqrt{2}}{1-\sqrt{2}}\) b)\(\dfrac{5\sqrt{6}-15}{6-2\sqrt{6}}\)

c) \(\sqrt{\left(3-2\sqrt{2}\right)\left(4-2\sqrt{3}\right)}\)

d) \(\sqrt{\left(6+2\sqrt{5}\right)^3}-\sqrt{\left(6-2\sqrt{5}\right)^3}\)

Answer 1

\(a.\dfrac{3-2\sqrt{2}}{1-\sqrt{2}}=\dfrac{2-2\sqrt{2}+1}{1-\sqrt{2}}=\dfrac{\left(1-\sqrt{2}\right)^2}{1-\sqrt{2}}=1-\sqrt{2}\)

\(b.\dfrac{5\sqrt{6}-15}{6-2\sqrt{6}}=\dfrac{-5\sqrt{3}\left(\sqrt{3}-\sqrt{2}\right)}{2\sqrt{3}\left(\sqrt{3}-\sqrt{2}\right)}=-\dfrac{5}{2}\)

\(c.\sqrt{\left(3-2\sqrt{2}\right)\left(4-2\sqrt{3}\right)}=\sqrt{2-2\sqrt{2}+1}.\sqrt{3-2\sqrt{3}+1}=\left(\sqrt{2}-1\right)\left(\sqrt{3}-1\right)\)

\(d.^3\sqrt{\left(6+2\sqrt{5}\right)^3}-^3\sqrt{\left(6-2\sqrt{5}\right)^3}=6+2\sqrt{5}-6+2\sqrt{5}=4\sqrt{5}\)