The value of is:

For any real numbers a and b, the difference-of-squares identity (a + b)(a − b) = a2 − b2 holds. This applies equally when a and b are surds, since squaring a square root removes the radical: (√n)2 = n for n ≥ 0.

1. Take a = √7 and b = √6 in the given expression (√7 + √6)(√7 − √6).

2. By the identity, (√7 + √6)(√7 − √6) = (√7)2 − (√6)2.

3. Since (√7)2 = 7 and (√6)2 = 6, this simplifies to 7 − 6 = 1.

4. Add the remaining constant term: 1 + 200 = 201.

Independently, √7 ≈ 2.6458 and √6 ≈ 2.4495, so the sum is ≈ 5.0953 and the difference ≈ 0.1963; their product ≈ 1.000, matching the algebraic result of 1 and confirming 1 + 200 = 201.

Hence the value of the expression is 201.