Order real numbers made from radicals: Let a = √6 − √5, b = √5 − 2, and c = 2 − √3. Choose the correct ascending order among a, b, and c.

Introduction / Context:
Comparing expressions with square roots is easier if you use approximate numeric values or monotonicity. This problem develops intuition for the relative sizes of numbers formed by differences involving radicals.

Given Data / Assumptions:

• a = √6 − √5
• b = √5 − 2
• c = 2 − √3
• All square roots use their principal (positive) values.

Concept / Approach:
Compute safe decimal approximations for the radicals to compare the magnitudes. √6 ≈ 2.449, √5 ≈ 2.236, and √3 ≈ 1.732. Then evaluate a, b, and c numerically and arrange them.

Step-by-Step Solution:

Verification / Alternative check:
The differences reflect that √6 − √5 is the smallest gap among listed pairs, while 2 − √3 is the largest of the three gaps; numerical values confirm the ordering.

Why Other Options Are Wrong:
Any other ordering contradicts the computed approximations and the monotonicity of the square root function.

Common Pitfalls:
Using overly rough approximations (e.g., √5 ≈ 2.2) can flip the order. Use at least three decimal places for reliable comparisons in close cases.

Final Answer:
a < b < c