The value of   $$\sqrt{75 + \sqrt{41 - \sqrt{21 + \sqrt{19 - \sqrt{9}}}}}$$​ is:

Correct option is A

​Given:

​$$\sqrt{75 + \sqrt{41 - \sqrt{21 + \sqrt{19 - \sqrt{9}}}}}$$​​

Solution:

​​$$\sqrt{75 + \sqrt{41 - \sqrt{21 + \sqrt{19 - \sqrt{9}}}}} \\ \ \\ = \sqrt{75 + \sqrt{41 - \sqrt{21 + \sqrt{19 - 3}}}}\\ \ \\ = \sqrt{75 + \sqrt{41 - \sqrt{21 + \sqrt{16}}}}\\ \ \\ = \sqrt{75 + \sqrt{41 - \sqrt{21 + 4}}}\\ \ \\ = \sqrt{75 + \sqrt{41 - \sqrt{25}}}\\ \ \\ = \sqrt{75 + \sqrt{41 - 5}}\\ \ \\ = \sqrt{75 + \sqrt{36}}\\ \ \\ = \sqrt{75 + 6}\\ \ \\ = \sqrt{81} \\ \ \\ = 9$$​​