What's the proper technique of converting 11 + 6sqrt(2) to the form [a+sqrt(b)]^2 ?

(a + √b)² = 11 + 6√2
a² + 2a√b + (√b)² = 11 + 6√2
a² + 2a√b + b = 11 + 6√2
(a² + b) + 2a√b = 11 + 6√2

Compare the rational and irrational parts on the both sides :
a² + b = 11 …… [1]
2a√b = 6√2 …… [2]

From [1] :
a² = 11 - b …… [3]

[2]² :
4a²b = 72
a²b = 18 …… [4]

Substitute [3] into [4] :
(11 - b)b = 18
11b - b² = 18
b² - 11b + 18 = 0
(b - 2)(b - 9) = 0
b = 2 or b = 9 (rejected for √9 = 3 is rational)

Substitute b = 2 into [3] :
a² = 11 - 2
a² = 9
a = 3 or a = -3 (rejected for a and b must be positive to make (a + √b)² = 11 + 6√2)

Hence, 11 + 6√2 = (3 + √2)²

[a + sqrt(b)]^2 = 11 + 6 sqrt (2)
a + sqrt (b) = 3.523380984562000931842152962703599841346703976961961345209...
If a = 2, b ≈ 2.3207
If a = 3, b ≈ 0.27393