Question

\(\sqrt{17+4\sqrt{15}}\) - \(\sqrt{8-2\sqrt{15}}\)

Answer 1

`sqrt{17+4sqrt15}-sqrt{8-2sqrt15}`

`=sqrt{12+2.2sqrt{3}.sqrt5+5}-sqrt{5-2sqrt{5.3}+3}`

`=sqrt{(2sqrt3+sqrt5)^2}-sqrt{(sqrt5-sqrt3)^2}`

`=|2sqrt3+sqrt5|-|sqrt5-sqrt3|`

`=2sqrt3+sqrt5-sqrt5+sqrt3=3sqrt3`

Answer 2

\(\sqrt{17+4\sqrt{15}}-\sqrt{8-2\sqrt{15}}\)

\(=2\sqrt{3}+\sqrt{5}-\sqrt{5}+\sqrt{3}\)

\(=3\sqrt{3}\)

Answer 3

Answer 4

\(\sqrt{17+4\sqrt{15}}-\sqrt{8-2\sqrt{15}}\)

\(=\sqrt{\left(\sqrt{12}+\sqrt{5}\right)^2}-\sqrt{\left(\sqrt{5}+\sqrt{3}\right)^2}\)

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