Evaluate √176 + √2401. Provide the exact simplified value where possible and give the final sum (rounded to two decimals if needed).

Introduction / Context:
This computation checks simplification of square roots and addition of an irrational and a perfect square root. It is a direct arithmetic task with careful simplification.

Given Data / Assumptions:

• Expression: √176 + √2401.
• 2401 is a perfect square (49^2).
• Round the final decimal to two places as necessary.

Concept / Approach:
Simplify each root separately. For perfect squares, take exact values. For non-perfect squares, factor out perfect square parts if possible, or evaluate numerically.

Step-by-Step Solution:
√2401 = 49 because 49^2 = 2401. For √176: factor 176 = 16 * 11, so √176 = √16 * √11 = 4√11. Approximate √11 ≈ 3.3166, thus √176 ≈ 4 * 3.3166 = 13.2664. Sum: √176 + √2401 ≈ 13.2664 + 49 = 62.2664. Rounded to two decimals: 62.27.

Verification / Alternative check:
A quick calculator check of √11 confirms ≈ 3.3166; multiplying by 4 and adding 49 reproduces ≈ 62.27.

Why Other Options Are Wrong:
64.00 and 60.00 are rounded guesses not supported by precise simplification. 56.50 is much too small; √2401 alone contributes 49.

Common Pitfalls:
Treating √176 as √169 (13) or √196 (14) is an error. Always factor to extract perfect squares or compute accurately.

Final Answer:
62.27