Submitted by Lee CP

Number Theory Level 3

There are 5 consecutive positive integers p, q, r, s, t , and each of them is smaller than 10000.

Given that, p+q+r+s+t= $a^{2}$ and q+r+s= $b^{3}$ , where a and b are integers.

What is the value of $\sqrt{p+q+r+s+t}$ ?