$$\sqrt{(6-\sqrt{37})^2} =$$

$$\sqrt{(6-\sqrt{37})^2} = |6 - \sqrt{37}| $$

Т.к. $$6 = \sqrt{36} < \sqrt{37}$$, то $$6 - \sqrt{37} < 0$$

$$|6 - \sqrt{37}| = - (6 - \sqrt{37}) = \sqrt{37} - 6$$

Ответ: $$\sqrt{37} - 6$$