Question

Rút gọn:

\(\sqrt{2}\) \(\sqrt{7-3\sqrt{5}}\)

Answer 1

\(\sqrt{2}\cdot\sqrt{7-3\sqrt{5}}=\sqrt{2\left(7-3\sqrt{5}\right)}\\ =\sqrt{14-6\sqrt{5}}\\ =\sqrt{9-2\cdot3\cdot\sqrt{5}+5}\\ =\sqrt{\left(3-\sqrt{5}\right)^2}=3-\sqrt{5}\)

Answer 2

\( \sqrt 2 .\sqrt {7 - 3\sqrt 5 } = \sqrt {2\left( {7 - 3\sqrt 5 } \right)} = \sqrt {14 - 6\sqrt 5 } = \sqrt {{3^2} - 2.3.\sqrt 5 + {{\sqrt 5 }^2}} = \sqrt {{{\left( {3 - \sqrt 5 } \right)}^2}} = 3 - \sqrt 5 \)