This questions can be answered with a calculator, but I have an impression it is meant to be a mental calculation problem, which can be solved as follows.
We know that 10*10=100, in otherwords, √ 100 = 10 which is greater than 9.4247.
We also know that √ 108 is greater than √ 100 =10
So we can conclude that
√ 108 > √ 100 = 10 > 9.4247
or simply
√ 108 > 9.4247
by the transitive property of logical propositions.
