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

1 Answer
Jun 4, 2018

Answer:

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#