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Question

The value of `sqrt(10+ sqrt(25 + sqrt( 108 + sqrt(154 + sqrt(225)))))`  is


Options:
A .  4
B .  6
C .  8
D .  10
Answer: Option A

Given exp.   `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.

     




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