Question

Answer 1

\(\sqrt{16-6\sqrt{7}}=\sqrt{9-2.3.\sqrt{7}+7}=\sqrt{\left(3-\sqrt{7}\right)^2}=\left|3-\sqrt{7}\right|=3-\sqrt{7}\)

Answer 2

`\sqrt{16-6 \sqrt{7} }`

\(=\sqrt{16-2.3\sqrt{7}}\)

\(=\sqrt{9-2.3\sqrt{7+7}}\)

`=`\(\sqrt{3^2-2.3\sqrt{7}+\left(\sqrt{7}\right)^2}\)

\(=\sqrt{\left(3-\sqrt{7}\right)^2}\)

\(=\left|3-\sqrt{7}\right|\)

\(=3-\sqrt{7}\)