Question

Rút gọn:

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)\(\left(2\sqrt{3}-5\sqrt{2}\right).\sqrt{3}-\sqrt{36}\)

d)\(3\sqrt{48}+2\sqrt{27}-\dfrac{1}{3}\sqrt{243}\)

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

f)\(4\sqrt{\dfrac{1}{2}}-\dfrac{6}{\sqrt{2}}\dfrac{2}{\sqrt{2}+1}\)

Answer 1

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

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

c) \(\left(2\sqrt{3}-5\sqrt{2}\right).\sqrt{3}-\sqrt{36}=6-5\sqrt{6}-6=5\sqrt{6}\)

d) \(3\sqrt{48}+2\sqrt{27}-\dfrac{1}{3}\sqrt{243}=12\sqrt{3}+6\sqrt{3}-3\sqrt{3}=15\sqrt{3}\)

e) \(6\sqrt{\dfrac{1}{3}}+\dfrac{9}{\sqrt{3}}-\dfrac{2}{\sqrt{3}-1}=2\sqrt{3}+3\sqrt{3}=\left(\sqrt{3}+1\right)=4\sqrt{3}-1\)

f) \(4\sqrt{\dfrac{1}{2}}-\dfrac{6}{\sqrt{2}}.\dfrac{2}{\sqrt{2}+1}=2\sqrt{2}-\left(12-6\sqrt{2}\right)=8\sqrt{2}-12\)