BT1 Rút gọn biểu thức đại số
a) \(2\sqrt{8}-3\sqrt{18}+\sqrt{32}\)
= \(4\sqrt{2}-9\sqrt{2}+4\sqrt{2}\)
= \(-\sqrt{2}\)
b)\(\sqrt{\left(1-\sqrt{2}\right)^2}+\sqrt{\left(1+\sqrt{2}\right)^2}\)
= \(\left|1-\sqrt{2}\right|+\left|1+\sqrt{2}\right|\)
= \(\sqrt{2}-1-\sqrt{2}-1\)
\(=-2\)
c) \(\left(\sqrt{45}-\sqrt{80}\right):\sqrt{5 }\)
= \(\left(3\sqrt{5}-4\sqrt{5}\right):\sqrt{5}\)
= \(-1\sqrt{5}:\sqrt{5}\)
= -1
d) \(\dfrac{3}{4+\sqrt{13}}-\dfrac{3}{4-\sqrt{13}}\)
\(=\dfrac{3\left(4-\sqrt{13}\right)}{\left(4-\sqrt{13}\right)\left(4+\sqrt{13}\right)}-\dfrac{3\left(4+\sqrt{13}\right)}{\left(4-\sqrt{13}\right)\left(4+\sqrt{13}\right)}\)
\(=\dfrac{12-3\sqrt{13}-12-3\sqrt{13}}{\left(4-\sqrt{13}\right)\left(4+\sqrt{13}\right)}\)
=\(\dfrac{-6\sqrt{13}}{16-13}\)
= \(\dfrac{-6\sqrt{13}}{3}=-2\sqrt{13}\)
\(e\ \sqrt{3}.\sqrt{27}-\dfrac{\sqrt{50}}{\sqrt{2}}\)
= 9 - 5 = 4
f) \(\sqrt{\left(2-\sqrt{3}\right)^2}-\sqrt{\left(-2\right)^2}\)
= \(\left|2-\sqrt{3}\right|+2\)
= \(\sqrt{3}-2+2\)
= \(\sqrt{3}\)
