Question

Thực hiện các phép tính sau a)căn(căn5-căn2)^2+căn(căn5+căn2)^2 b)căn(căn2+1)^2-căn(căn2-5)^2

Answer 1

a) \(\sqrt{\left(\sqrt{5}-\sqrt{2}\right)^2}+\sqrt{\left(\sqrt{5}+\sqrt{2}\right)^2}\)

\(=\left|\sqrt{5}-\sqrt{2}\right|+\left|\sqrt{5}+\sqrt{2}\right|\)

\(=\sqrt{5}-\sqrt{2}+\sqrt{5}+\sqrt{2}\)

\(=\sqrt{5}+\sqrt{5}\)

\(=2\sqrt{5}\)

b) \(\sqrt{\left(\sqrt{2}-1\right)^2}-\sqrt{\left(\sqrt{2}-5\right)^2}\)

\(=\left|\sqrt{2}-1\right|-\left|\sqrt{2}-5\right|\)

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

\(=\sqrt{2}-1-5+\sqrt{2}\)

\(=2\sqrt{2}-6\)