Question

rút gọn các biểu thức ( không dùng máy tính bỏ túi)

a) 2\(\sqrt{98}-3\sqrt{18}+\dfrac{1}{2}\sqrt{32}\)

b)\(\left(5\sqrt{2}+2\sqrt{5}\right).\sqrt{5}-\sqrt{250}\)

c) \(6\sqrt{\dfrac{1}{3}}+\dfrac{9}{\sqrt{3}}-\dfrac{2}{\sqrt{3}-1}\)

Answer 1

a) \(2\sqrt{98}-3\sqrt{18}+\dfrac{1}{2}\sqrt{32}=2\sqrt{2.49}-3\sqrt{2.9}+\dfrac{1}{2}\sqrt{2.16}=14\sqrt{2}-9\sqrt{2}+2\sqrt{2}=7\sqrt{2}\)

b) \(\left(5\sqrt{2}+2\sqrt{5}\right).\sqrt{5}-\sqrt{250}=5\sqrt{2}.\sqrt{5}+2\sqrt{5}.\sqrt{5}-\sqrt{250}=5\sqrt{2.5}+2\sqrt{5.5}-\sqrt{250}\) = \(5.\sqrt{10}+10-\sqrt{250}\)

c) \(6\sqrt{\dfrac{1}{3}}+\dfrac{9}{\sqrt{3}}-\dfrac{2}{\sqrt{3}-1}\)

= \(\dfrac{6\sqrt{\dfrac{1}{3}}\sqrt{3}\left(\sqrt{3}-1\right)+9\left(\sqrt{3}-1\right)-2}{\sqrt{3}\left(\sqrt{3}-1\right)}=\dfrac{6\sqrt{3}-1+9\sqrt{3}-9-2}{2}=\dfrac{15\sqrt{3}-12}{2}\)