Question

2. Find the mean proportional of 6 and 216.
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Answer 1

Answer:

36

Step-by-step explanation:

Let the middle term be x

According to theory, if a, b, c are in mean proportion then

${b}^{2} = ac$

Thus, by using that if 6,x,216 are in proportion the

${ x}^{2} = 6 \times 216 \\ {x}^{2} = 6 \times {6}^{3} \\ {x}^{2} = {6}^{2} \times {6}^{2} \\ x = \sqrt{ {6}^{2} \times {6}^{2} } \\ = \sqrt{36 \times 36} \\ = 36$

Thus the mean proportion of 6 and 216 is 36