Bài 2: phân tích các biểu thức sau thành tích
a) 5 + \(\sqrt{5}\)
b) \(\sqrt{33}+\sqrt{22}\)
c) \(\sqrt{15}-\sqrt{6}\)
d) 10 + \(2\sqrt{10}\)
e) a - b với a, b \(\ge\) 0
f)a - 4 với a \(\ge\) 0
g) 3 - x
Bài 3: rút gọn các biểu thức
a) \(\dfrac{a}{b}\sqrt{\dfrac{a^2}{b^4}}\) a > 0 , b \(\ne\) 0
b) 2\(a^2\sqrt{\dfrac{b^2}{4a^2}}\) với b <0
a) \(5+\sqrt{5}=\sqrt{5}\left(\sqrt{5}+1\right)\)
b) \(\sqrt{33}+\sqrt{22}=\sqrt{11}.\sqrt{3}+\sqrt{11}.\sqrt{2}=\sqrt{11}\left(\sqrt{3}+\sqrt{2}\right)\)
c) \(\sqrt{15}-\sqrt{6}=\sqrt{3}.\sqrt{5}-\sqrt{3}.\sqrt{2}=\sqrt{3}\left(\sqrt{5}-\sqrt{2}\right)\)
d) \(10+2\sqrt{10}=\sqrt{10}\left(\sqrt{10}+2\right)\)
e) \(a-b=\left(\sqrt{a}-\sqrt{b}\right)\left(\sqrt{a}+\sqrt{b}\right)\)
f) \(a-4=\left(\sqrt{a}-2\right)\left(\sqrt{a}+2\right)\)
g) \(3-x=\left(\sqrt{3}-\sqrt{x}\right)\left(\sqrt{3}+\sqrt{x}\right)\)
Rút gọn
a) \(\dfrac{a}{b}\sqrt{\dfrac{a^2}{b^4}}=\dfrac{a}{b}.\dfrac{a}{b^2}=\dfrac{a^2}{b^3}\)
b) Ta có b<0\(\Rightarrow\sqrt{b^2}=-b\)
\(2a^2\sqrt{\dfrac{b^2}{4a^2}}=\dfrac{2a^2.\left(-b\right)}{2a}=-ab\)
