Question

tính \(\left(3\sqrt{2}\right)^2\sqrt{\dfrac{2}{16-6\sqrt{7}}}\)

Answer 1

`(3\sqrt2)^2.\sqrt(2/(16-6\sqrt7))`

`=18. \sqrt(2/(9-6\sqrt7+7))`

`=18 .\sqrt(2/(3^2-2.3.\sqrt7+\sqrt7^2))`

`=18 .\sqrt(2/((3-\sqrt7)^2))`

`= 18. \sqrt2/(3-\sqrt7)`

`=18 . (\sqrt14+3\sqrt2)/2`

`=9+\sqrt14+27\sqrt2`

Answer 2

\(\left(3\sqrt{2}\right)^2\cdot\sqrt{\dfrac{2}{16-6\sqrt{7}}}\)

\(=18\cdot\dfrac{\sqrt{2}}{3-\sqrt{7}}\)

\(=\dfrac{18\sqrt{2}}{3-\sqrt{7}}=9\sqrt{14}+27\sqrt{2}\)