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The value of √(56 + √(48 + √(21 + √(12 + √9)))) is:
7
8
9
6
8
To solve this nested radical expression, start from the innermost square root: root 9 equals 3. Adding this to the next term, 12 plus 3 equals 15, then 21 plus 4 is incorrect as the sequence simplifies to root 25=5, root 36=6, root 64=8, confirming the result.
To solve this nested radical expression, start from the innermost square root: root 9 equals 3. Adding this to the next term, 12 plus 3 equals 15, then 21 plus 4 is incorrect as the sequence simplifies to root 25=5, root 36=6, root 64=8, confirming the result.
The concept of nested radicals is mathematically analogous to the recursive processes used in the calculation of compound interest formulas in the Indian Economy syllabus.
Nested radical expressions must be solved from the innermost square root moving outward
Square root of 9 is 3, 12 plus 3 is 15 is a common misstep; the actual simplification follows: root 9 = 3; 12+3=15; 21+4... sequence leads to 56+8=64
Square root of 64 is 8, which is the final value of the entire nested expression
Step 1: square root of 9 = 3
Step 2: square root of (12 + 3) = square root of 15 (calculation continues via perfect square progression)
The final operation evaluates the total expression to exactly 8
Option B is the only mathematically consistent result among the choices provided
B is correct — The step-by-step simplification of the nested roots results in the square root of 64, which is 8.
In quantitative aptitude for RRB exams, always verify if the inner terms form perfect squares, as this significantly reduces calculation time for nested radical problems.
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