Submitted by Lee CP

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=a2a^{2} and q+r+s=b3b^{3}, where a and b are integers.

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

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