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Insert seven geometric means between 2 and 162.

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Let ` G_(1) , G_(2) , G_(3) ,… G_(7)` be the seven geometric means between 2 and 162
Then ` 2. G_(1), G_(2), G_(3), … G_(7)` 162 are in G.P. with common ratio
`r = ((162)/(2))^((1)/(7+1)) = (81)^((1)/(8)) = [(sqrt(3))^(8)]^((1)/(8)) = sqrt(3)`
` therefore G_(1) = 2 sqrt(3) , G_(2) = 6, G_(3) = 6sqrt(3), G_(4) = 18, G_(5) = 18sqrt(3), G_(6) = 54 , G_(7) = 54sqrt(3)`
Hence , seven geometric means between 2 and 162 are
`2sqrt(3),6,6sqrt(3), 18,18sqrt(3), 54 and 54sqrt(3)`
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