Question

Answer 1

4).

\(=\sqrt{12-6\sqrt{3}}+\sqrt{21-12\sqrt{3}}\)

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

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

 

 

Answer 2

5).

\(=\dfrac{\sqrt{2\left(4-2\sqrt{3}\right)}}{\sqrt{3}-1}.2\sqrt{2}=\dfrac{\sqrt{2\left(\sqrt{3}-1\right)^2}}{\sqrt{3}-1}\)

\(=\dfrac{\sqrt{2}\left(\sqrt{3}-1\right)}{\sqrt{3}-1}.2\sqrt{2}=\sqrt{2}-2\sqrt{2}=-\sqrt{2}\)

6).

\(=\dfrac{\sqrt{\left(4-2\sqrt{3}\right)^2}}{\sqrt{3}-1}=\dfrac{4-2\sqrt{3}}{\sqrt{3}-1}=\dfrac{\left(\sqrt{3}-1\right)^2}{\sqrt{3}-1}=\sqrt{3}-1\)