Question

Rút gọn

a. 2 căn10+căn30-2 căn2-căn6/2 căn10-2 căn 2
b. căn((1-căn2006)^2) x căn(2007+2 căn2006 )

Answer 1

a: Ta có: \(\dfrac{2\sqrt{10}+\sqrt{30}-2\sqrt{2}-\sqrt{6}}{2\sqrt{10}-2\sqrt{2}}\)

\(=\dfrac{\sqrt{10}\left(2+\sqrt{3}\right)-\sqrt{2}\left(2+\sqrt{3}\right)}{2\sqrt{2}\left(\sqrt{5}-1\right)}\)

\(=\dfrac{\sqrt{2}\left(2+\sqrt{3}\right)\left(\sqrt{5}-1\right)}{2\sqrt{2}\left(\sqrt{5}-1\right)}\)

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

b) Ta có: \(\sqrt{\left(1-\sqrt{2006}\right)^2}\cdot\sqrt{2007+2\sqrt{2006}}\)

\(=\left(\sqrt{2006}-1\right)\left(\sqrt{2006}+1\right)\)

=2005