解析
|p|=2√3
|q|=√3
|a+b|=√(a+b)²
=√(5p+2q+p-3q)²
=√(6p-q)²
=√(36p²-12pq+q²)
=√(36*8-12*6√2*√2/2+9
=√288-72+9
=√225
=15