Question

Tính:

a) \(3\sqrt{7}\left(2\sqrt{7}-3\right)^2\)

b) \(\left(\sqrt{\dfrac{2}{3}}-\sqrt{\dfrac{3}{2}}\right)^2\)

c) \(\left(\sqrt{3}-\sqrt{2}\right)\left(\sqrt{6}+2\right)\)

Answer 1

a, \(3\sqrt{7}\left(2\sqrt{7}-3\right)^2\)

\(=3\sqrt{7}.\left[\left(2\sqrt{7}\right)^2-12\sqrt{7}+9\right]\)

\(=3\sqrt{7}.\left(28-12\sqrt{7}+9\right)\)

\(=84\sqrt{7}-252+27\sqrt{7}=111\sqrt{7}-252\)

b, \(\left(\sqrt{\dfrac{2}{3}}-\sqrt{\dfrac{3}{2}}\right)^2\)

\(=\dfrac{2}{3}-2\sqrt{\dfrac{2}{3}.\dfrac{3}{2}}+\dfrac{3}{2}=\dfrac{2}{3}-2+\dfrac{3}{2}=\dfrac{1}{6}\)

c, \(\left(\sqrt{3}-\sqrt{2}\right)\left(\sqrt{6}+2\right)\)

\(=\sqrt{18}+2\sqrt{3}-\sqrt{12}-2\sqrt{2}\)

Chúc bạn học tốt!!!

Answer 2

câu c) \(\left(\sqrt{3}-\sqrt{2}\right)\left(\sqrt{6}+2\right)=\left(\sqrt{3}-\sqrt{2}\right).\left(\sqrt{3}+\sqrt{2}\right).\sqrt{2}\)

\(=\left(\left(\sqrt{3}\right)^2-\left(\sqrt{2}\right)^2\right)\sqrt{2}=\left(3-2\right).\sqrt{2}=1.\sqrt{2}=\sqrt{2}\)