Question

căn(10+5căn3)-căn(10-5căn3)

Answer 1

`sqrt{10+5sqrt3}>sqrt{10-5sqrt3}`

`=>sqrt{10+5sqrt3}-sqrt{10-5sqrt3}>0`

`=>A>0`

`A=sqrt{10+5sqrt3}-sqrt{10-5sqrt3}`

`<=>A^2=10+5sqrt3+10-5sqrt3-2sqrt{(10+5sqrt3)(10-5sqrt3)}`

`<=>A^2=20-2sqrt{100-75}=20-2sqrt{25}`

`<=>A^2=20-2.5=10`

`<=>A=sqrt10`(do `A>0`)

Answer 2

Ta có: \(\sqrt{10+5\sqrt{3}}-\sqrt{10-5\sqrt{3}}\)

\(=\dfrac{\sqrt{20+10\sqrt{3}}-\sqrt{20-10\sqrt{3}}}{\sqrt{2}}\)

\(=\dfrac{\sqrt{15}+\sqrt{5}-\sqrt{15}+\sqrt{5}}{\sqrt{2}}\)

\(=\sqrt{10}\)