Question

Giúp mìnk câu d

Answer 1

`d)sqrt{7-2sqrt{10}}-sqrt{7+2sqrt{10}}`

`=sqrt{5-2sqrt{5}.sqrt2+2}-sqrt{5+2sqrt{5}.sqrt2+2}`

`=sqrt{(sqrt5-sqrt2)^2}-sqrt{(sqrt5+sqrt2)^2}`

`=sqrt5-sqrt2-sqrt5-sqrt2=-2sqrt2`

Answer 2

d, \(\sqrt{7-2\sqrt{10}}-\sqrt{7+2\sqrt{10}}=\sqrt{5-2.\sqrt{2}.\sqrt{5}+2}-\sqrt{5+2.\sqrt{2}.\sqrt{5}+2}\)

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

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

Answer 3

d) Ta có: \(\sqrt{7-2\sqrt{10}}-\sqrt{7+2\sqrt{10}}\)

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

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