Let the given expression be $E = \sqrt{31\times32\times30\times33+1}$. We can rearrange the terms as $E = \sqrt{30\times31\times32\times33+1}$. Let $x = 30$. Then the expression becomes $E = \sqrt{x(x+1)(x+2)(x+3)+1}$. We can group the terms: $E = \sqrt{[x(x+3)][(x+1)(x+2)]+1}$. This simplifies to $E = \sqrt{(x^2+3x)(x^2+3x+2)+1}$. Let $y = x^2+3x$. Substituting $y$ into the expression, we get: $E = \sqrt{y(y+2)+1}$ $E = \sqrt{y^2+2y+1}$ $E = \sqrt{(y+1)^2}$ $E = |y+1|$ Since $x=30$, $y = 30^2+3(30) = 900+90 = 990$. Therefore, $E = |990+1| = 991$. Thus, the value of the expression is $991$.