Question

Rút gọn

a) \(\dfrac{2-\sqrt{2}}{\sqrt{2}}\)

b) \(\sqrt{\dfrac{x-49}{\sqrt{x}-7}}\)

c) \(\sqrt{7-2\sqrt{6}}\)

d) \(\sqrt{4+2\sqrt{3}}\)

e) \(\sqrt{13-14\sqrt{3}}\)

Answer 1

a)\(\dfrac{2-\sqrt{2}}{\sqrt{2}}\)

\(\Leftrightarrow\dfrac{\sqrt{2}\left(\sqrt{2}-1\right)}{\sqrt{2}}\)

\(\Leftrightarrow\sqrt{2}-1\)

b)\(\sqrt{\dfrac{x-49}{\sqrt{x}-7}}\)

\(\Leftrightarrow\sqrt{\dfrac{\left(\sqrt{x}-7\right)\left(\sqrt{x}+7\right)}{\sqrt{x}-7}}\)

\(\Leftrightarrow\sqrt{\sqrt{x}+7}\)

c)\(\sqrt{7-2\sqrt{6}}\)

\(\Leftrightarrow\sqrt{6-2\sqrt{6}+1}\)

\(\Leftrightarrow\sqrt{\left(\sqrt{6}-1\right)^2}\)

\(\Leftrightarrow\sqrt{6}-1\)

d)\(\sqrt{4+2\sqrt{3}}\)

\(\Leftrightarrow\sqrt{\left(\sqrt{3}+1\right)^2}\)

\(\Leftrightarrow\sqrt{3}+1\)

e)\(\sqrt{13-14\sqrt{3}}\)

Câu này có dư số 1 ở chỗ 14 phải k bn ???