Question

How do you simplify `root4(93)*sqrt(92)`?

Answer 1

You can use logarithms if your calculator cannot do higher-order roots directly.
`29.787`

Explanation:

`.^4√93⋅√92` = `1/4log(93) + 1/2log(92)`

Logarithm tables are readily available online and in libraries.

`1/4log(93) + 1/2log(92)` = `1/4(1.9685) + 1/2(1.9638)`

`0.4921 + 0.9819 = 1.4740`
To convert this back to the desired number, use the exponential function (inverse of logarithm):`exp(1.4740) = 10^(1.4740) = 29.787`

Direct calculator calculation:
`3.1054 xx 9.5917 = 29.787`