If p is the third proportional to 6 and 18, and q is the third proportional to p and 54, find the value of q.
54
The third proportional to two numbers \(a\) and \(b\) is the value \(x\) such that \(a:b = b:x\).
For p as the third proportional to 6 and 18: \(6:18 = 18:p\), so \(p = \frac{18 \times 18}{6} = 54\).
Now q is the third proportional to p (=54) and 54: \(54:54 = 54:q\), so \(q = \frac{54 \times 54}{54} = 54\).
Hence, the value of q is 54.
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