Suppose that a, b, and c are real numbers such that a/b = sqrt(10)/sqrt(21) and b/c = sqrt(14)/sqrt(15). Find a/c. Completely simplify and rationalize the denominator.
a/c = [ a/b ] / [ c/b ] = [ sqrt(10) / sqrt(21) ] / [ sqrt(15) / sqrt(14) ]
= [ sqrt(10) · sqrt(14) ] / [ sqrt(21) · sqrt(15) ]
= [ sqrt(10) / sqrt(15) ] · [ sqrt(14) / sqrt(21) ]
= [ sqrt(2) / sqrt(3) ] · [ sqrt(2) / sqrt(3) ]
= 2/3
