Question

tính

\(\sqrt{2}.\sqrt{4-\sqrt{7}}\)

giúp mình với

Answer 1

\(=\sqrt{8-2\sqrt{7}}\)

\(=\sqrt{7-2\sqrt{7}+1}\)

\(=\sqrt{\left(\sqrt{7}-1\right)^2}\)

Answer 2

\(\sqrt{2}.\sqrt{4-\sqrt{7}}\\ =\dfrac{1}{2}.\sqrt{2}.\sqrt{8-2\sqrt{7}}\\ =\dfrac{1}{2}.\sqrt{2}.\sqrt{7-2\sqrt{7}.1+1}\\ =\dfrac{1}{2}.\sqrt{2}.\sqrt{\left(\sqrt{7}-1\right)^2}\\ =\dfrac{1}{2}.\sqrt{2}.\left(\sqrt{7}-1\right)\\ =\dfrac{1}{2}.\sqrt{2}.\sqrt{7}-\dfrac{1}{2}.\sqrt{2}\\ =\dfrac{1}{2}.\sqrt{14}-\dfrac{1}{2}.\sqrt{2}\\ =\dfrac{1}{2}.\left(\sqrt{14}-\sqrt{2}\right)\)