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

Correct option is A

Given:

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

Solution:

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

=$$\sqrt{10+\sqrt{25+\sqrt{108+\sqrt{154+15}}}}$$​

=$$\sqrt{10+\sqrt{25+\sqrt{108+\sqrt{169}}}}$$

=$$\sqrt{10+\sqrt{25+\sqrt{108+13}}}$$

=$$\sqrt{10+\sqrt{25+\sqrt{121}}}$$

=$$\sqrt{10+\sqrt{25+11}}$$

=$$\sqrt{10+\sqrt{36}}$$

=$$\sqrt{10+6}$$

=$$\sqrt{16}=4$$​​