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Question
If `root(3)(1906624) xx sqrt(x)` = 3100, find x
Solution
`root(3)(1906624) xx sqrt(x)` = 3100
`root(3)(2 xx 2 xx 2 xx 2 xx 2 xx 2 xx 31 xx 31 xx 31) xx sqrt(x)` = 3100
`root(3)(2^3 xx 2^3 xx 31^3) xx sqrt(x)` = 3100
`2 xx 2 xx 31 xx sqrt(x)` = 3100
`sqrt(x) = 3100/(2 xx 2 xx 31)`
= `3100/(2 xx 2 xx 31)`
`sqrt(x)` = 25
Squaring on both sides
`(sqrt(x))^2` = 252
x = 625
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