The value of $$\sqrt{10 + \sqrt{25 + \sqrt{108 + \sqrt{154 + \sqrt{225}}}}}$$ is ?​

Correct option is A

We are given a nested square root expression:

​$$\sqrt{10 + \sqrt{25 + \sqrt{108 + \sqrt{154 + \sqrt{225}}}}}$$​​

Let's evaluate from the innermost root outward:

• 225=15\sqrt{225} = 15225​=15​

• 154+15=169=13\sqrt{154 + 15} = \sqrt{169} = 13154+15​=169​=13​

• 108+13=121=11\sqrt{108 + 13} = \sqrt{121} = 11108+13​=121​=11​

• 25+11=36=6\sqrt{25 + 11} = \sqrt{36} = 625+11​=36​=6​

• 10+6=16=4\sqrt{10 + 6} = \sqrt{16} = 410+6​=16​=4​

Final answer: (A) 4