Question

\(\sqrt{13-4\sqrt{3}}\)

 

Answer 1

\(=\sqrt{12-2.\sqrt{12.1}+1}=\sqrt{\left(\sqrt{12}-1\right)^2}=\sqrt{12}-1=2\sqrt{3}-1\)

Answer 2

\(\sqrt{13-4\sqrt[]{3}}=\sqrt{\left(2\sqrt[]{3}\right)^2-2.2\sqrt[]{3}.1+1^2}=\sqrt[]{\left(2\sqrt[]{3}-1\right)^2}=\left|2\sqrt[]{3}-1\right|=2\sqrt[]{3}-1\left(2\sqrt[]{3}>1\Rightarrow8>1\right)\)