Question

Chứng minh:

\(\sqrt{10+\sqrt{19}}.\sqrt{10-\sqrt{19}}\) = 9

Answer 1

\(\sqrt{10+\sqrt{19}}+\sqrt{10-\sqrt{19}}\)

\(=\sqrt{10^2-\left(\sqrt{19}\right)^2}\)

\(=\sqrt{100-19}\)

= \(\sqrt{81}\)

\(=9\)

Answer 2

\(\sqrt{10+\sqrt{19}}+\sqrt{10-\sqrt{19}}\)

=\(\sqrt{10^2-\left(\sqrt{19}\right)^2}\)

=\(\sqrt{100-19}\)

=\(\sqrt{81}\)

= 9 (đpcm)