Question

rút gọn biểu thức k dùng máy tính bỏ túi

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

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

Answer 1

\(a,A=5\sqrt{10}-10-5\sqrt{10}\\ =-10\\ b,B=2\sqrt{3}+3\sqrt{3}-\dfrac{\sqrt{3}+1}{2}\\ =5\sqrt{3}-\dfrac{\sqrt{3}+1}{2}\\ =\dfrac{10\sqrt{3}-\sqrt{3}-1}{2}\\ =\dfrac{9\sqrt{3}-1}{2}\)

Answer 2

a , \(\left(5\sqrt{2}-2\sqrt{5}\right)\sqrt{5}\) - \(\sqrt{250}\)

= \(5\sqrt{10}-2.5-5\sqrt{10}=-2.5=-10\)

b , \(6\sqrt{\dfrac{1}{3}}+\dfrac{9}{\sqrt{3}}-\dfrac{2}{\sqrt{3}-1}=\dfrac{15}{\sqrt{3}}-\dfrac{2}{\sqrt{3}-1}\)

= \(\dfrac{5\sqrt{3}\left(\sqrt{3}-1\right)-2}{\sqrt{3}-1}=\dfrac{13-5\sqrt{3}}{\sqrt{3}-1}\)