Suppose that a, b, and c are real numbers such that $\frac{a}{b} = \frac{\sqrt{10}}{\sqrt{21}}$ and $\frac{b}{c} = \frac{\sqrt{135}}{\sqrt{42}}$. Find $\frac{a}{c}$. Completely simplify and rationalize the denominator.
+130071 a/b * b/c = a / c = sqrt (10) / sqrt (42) * sqrt (135) / sqrt (42) =
sqrt (2) sqrt (5) sqrt (5 ) sqrt (27)
_____________ * _______________ =
sqrt (2) sqrt (21) sqrt (2) sqrt (21)
5 sqrt (27)
_____________ =
21 sqrt (2)
5 sqrt (27) sqrt (2)
_______________ =
21 sqrt (2) sqrt (2)
5 sqrt (54)
_________ =
42
5 sqrt (9) sqrt (6)
_____________ =
42
15 sqrt (6)
________ =
42
5 sqrt (6)
________
14
