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The value of √(11 + √(21 + √(16 + √(20 + √16))))) is:
3
4
5
6
4
The value of the nested radical expression is evaluated step by step from the innermost square root to the outermost square root. Starting with the innermost square root of 16 which is 4, adding it successively and taking square roots leads to the final simplified value of 4.
The value of the nested radical expression is evaluated step by step from the innermost square root to the outermost square root. Starting with the innermost square root of 16 which is 4, adding it successively and taking square roots leads to the final simplified value of 4.
Mathematical operations and simplification techniques form a core pillar of quantitative aptitude tested across all Indian competitive recruitment examinations including RRB JE and NTPC.
Nested radicals are evaluated from the inside out starting with the innermost radical term.
The square root of 16 equals 4, which is then added to the preceding term under the radical.
Repeated simplification yields a clean integer value confirming the correct option as 4.
Option A (3) is incorrect because the final evaluated value is higher than 3.
Option B (4) is the correct choice as it matches the final simplified result of the nested square root sequence.
Option C (5) and Option D (6) overestimate the value derived from the step-by-step reduction of the expression.
B is correct — 4 is the exact evaluated value of the nested radical expression.
Mastering surds and indices shortcuts alongside nested radical reduction helps solve complex quantitative sections efficiently in RRB CBT-1 examinations.
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