MathNet 2026 — Part 07 Question 149

If $36-4 \sqrt{2}-6 \sqrt{3}+12 \sqrt{6}=(a \sqrt{2}+b \sqrt{3}+c)^{2}$, find the value of $a^{2}+b^{2}+c^{2}$.


(a) 12

(c) 14

(b) 5

(d) 6