Question

giúp mình vs

Answer 1

a: \(=3\sqrt{2}\left(6\sqrt{2}-8\sqrt{2}-16\sqrt{2}\right)\)

\(=3\sqrt{2}\cdot\left(-18\right)\sqrt{2}=-108\)

b: \(=\sqrt{12-18}=\sqrt{-6}\)

=>Biểu thức vô nghĩa

c: \(=\dfrac{\sqrt{6-2\sqrt{5}}-\sqrt{6+2\sqrt{5}}}{\sqrt{2}}\)

\(=\dfrac{\sqrt{5}-1-\sqrt{5}-1}{\sqrt{2}}=-\sqrt{2}\)

Answer 2

Tham khảo (Trong quá trình làm, do lười nên sẽ thiếu bước đó.)

a) 3\(\sqrt{2}\)(\(\sqrt{72}\)-2\(\sqrt{32}\)-2\(\sqrt{128}\))

=3\(\sqrt{2}\)(\(\sqrt{2\cdot36}\)-2\(\sqrt{2\cdot16}\)-2\(\sqrt{2\cdot64}\)

=3\(\sqrt{2}\)(6\(\sqrt{2}\)-8\(\sqrt{2}\)-16\(\sqrt{2}\))

=\(3\sqrt{2}\cdot\left(-18\sqrt{2}\right)\)

=-108

b)\(\sqrt{2\sqrt{3}+3\sqrt{2}}\)\(\cdot\)\(\sqrt{2\sqrt{3}-3\sqrt{2}}\)

=\(\sqrt{\left(2\sqrt{3}+3\sqrt{2}\right)\cdot\left(2\sqrt{3}-3\sqrt{2}\right)}\)

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

=\(\sqrt{12-18}\)

=\(\sqrt{-6}\)(?)(Mình nghĩ câu này đề bài sai sao ý, mình tính đi tính lại vẫn ra kết quả này)

c)\(\sqrt{3-\sqrt{5}}-\sqrt{3+\sqrt{5}}\)(Mình không làm được câu này nhưng nếu là\(\sqrt{3-\sqrt{5}}\cdot\sqrt{3+\sqrt{5}}\) thì mình làm được)

d)\(\dfrac{2\sqrt{3}}{\sqrt{2}+\sqrt{3}+\sqrt{5}}+\dfrac{2}{\sqrt{6}+\sqrt{10}}\)

=\(\dfrac{2\sqrt{3}}{\sqrt{2}+\sqrt{3}+\sqrt{5}}+\dfrac{\sqrt{2}\cdot\sqrt{2}}{\sqrt{2}\cdot\left(\sqrt{3}+\sqrt{5}\right)}\)

=\(\dfrac{2\sqrt{3}}{\sqrt{2}+\sqrt{3}+\sqrt{5}}+\dfrac{\sqrt{2}}{\sqrt{3}+\sqrt{5}}\)

=\(\dfrac{2\sqrt{3}\left(\sqrt{3}+\sqrt{5}\right)}{\left(\sqrt{2}+\sqrt{3}+\sqrt{5}\right)\left(\sqrt{3}+\sqrt{5}\right)}+\dfrac{\sqrt{2}\left(\sqrt{2}+\sqrt{3}+\sqrt{5}\right)}{\left(\sqrt{2}+\sqrt{3}+\sqrt{5}\right)\left(\sqrt{3}+\sqrt{5}\right)}\)

=\(\dfrac{2\sqrt{3}\left(\sqrt{3}+\sqrt{5}\right)+\sqrt{2}\left(\sqrt{2}+\sqrt{3}+\sqrt{5}\right)}{\left(\sqrt{2}+\sqrt{3}+\sqrt{5}\right)\left(\sqrt{3}+\sqrt{5}\right)}\)

=\(\dfrac{6+2\sqrt{15}+4+\sqrt{6}+\sqrt{10}}{\left(\sqrt{2}+\sqrt{3}+\sqrt{5}\right)\left(\sqrt{3}+\sqrt{5}\right)}\)

=\(\dfrac{10+2\sqrt{15}+\sqrt{6}+\sqrt{10}}{\left(\sqrt{2}+\sqrt{3}+\sqrt{5}\right)\left(\sqrt{3}+\sqrt{5}\right)}\)

=\(\dfrac{2\sqrt{5}\left(\sqrt{3}+\sqrt{5}\right)+\sqrt{2}\left(\sqrt{3}+\sqrt{5}\right)}{\left(\sqrt{2}+\sqrt{3}+\sqrt{5}\right)\left(\sqrt{3}+\sqrt{5}\right)}\)

=\(\dfrac{\left(\sqrt{3}+\sqrt{5}\right)\left(2\sqrt{5}+\sqrt{2}\right)}{\left(\sqrt{2}+\sqrt{3}+\sqrt{5}\right)\left(\sqrt{3}+\sqrt{5}\right)}\)

=\(\dfrac{2\sqrt{5}+\sqrt{2}}{\sqrt{2}+\sqrt{3}+\sqrt{5}}\)(Không biết có rút gọn được nữa không nhưng mỏi tay rùi)