Use Those Radicals Sparingly!

Algebra Level 5

1+2++100\large \sqrt{1}+\sqrt{2}+\cdots+\sqrt{100}

If the sum above can be expressed as

a0+a1b1+a2b2++anbna_0 + a_1 \sqrt{b_1} + a_2 \sqrt{b_2} + \cdots + a_n \sqrt{b_n}

where a0,a1,a2,,an,b1,b2,,bna_0, a_1, a_2, \ldots, a_n, b_1, b_2, \ldots, b_n are integers, what is the minimum value of nn?

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