Addition inside root problem

Question

Help me calculate the answer for$$ \sqrt{3+\sqrt 5}\cdot \sqrt{3-\sqrt 5}$$ (NO CALCULATOR ALLOWED). The answer in the book is "2" but I don't know how they solved it.

Answer 1

Remember these rules:

• $\sqrt A\times \sqrt B=\sqrt {AB}, ~ A,B≥0$

• $(A-B)(A+B)=A^2-B^2$

Then you can start:

$$\sqrt {A+\sqrt B}× \sqrt {A-\sqrt B}=\sqrt {(A+\sqrt B)×(A-\sqrt B)}=...$$