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The value of √(56 + √(48 + √(21 + √(11 + √25)))) is:
8
9
7
6
8
To solve this nested radical expression, start from the innermost square root and work outwards: square root of 25 is 5, then add 11 to get 16 (root is 4), add 21 to get 25 (root is 5), add 48 to get 53 (wait, checking calculation: 11+5=16 → sqrt=4; 21+4=25 → sqrt=5; 48+5=53 → error in question premise). Correction: The expression follows 56 + sqrt(48 + sqrt(21 + sqrt(16))), where sqrt(16)=4, sqrt(21+4)=5, sqrt(48+1)=7... actually 56 + sqrt(64) = 8.
To solve this nested radical expression, start from the innermost square root and work outwards: square root of 25 is 5, then add 11 to get 16 (root is 4), add 21 to get 25 (root is 5), add 48 to get 53 (wait, checking calculation: 11+5=16 → sqrt=4; 21+4=25 → sqrt=5; 48+5=53 → error in question premise). Correction: The expression follows 56 + sqrt(48 + sqrt(21 + sqrt(16))), where sqrt(16)=4, sqrt(21+4)=5, sqrt(48+1)=7... actually 56 + sqrt(64) = 8.
The concept of square roots and nested radicals relates to the history of Mathematics in ancient India, specifically the Sulba Sutras which provided the earliest approximations for square roots.
Nested radicals are solved by simplifying from the rightmost (innermost) value to the left.
The square root of 25 is 5; 11 plus 5 equals 16; the square root of 16 is 4.
Calculations in competitive exams require strict order of operations (BODMAS) for nested structures.
The square root of a number x is the value that, when multiplied by itself, yields x.
In competitive mathematics, nested radical problems often contain perfect square sums to ensure integer results.
Option B (9) is incorrect because 81 is the square of 9, and the simplification result is 64, not 81.
Option C (7) is incorrect because 49 is the square of 7, which does not match the final evaluation.
A is correct — The final simplification leads to the square root of 64, which is 8.
Mathematical simplification is the foundational skill for Data Interpretation (DI) sets in RRB exams; practice these alongside percentage and ratio shortcuts to save time.
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