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This problem requires students to engage with the relationship between algebra, graphs and the physical processes from which they are derived. There is a strong modelling aspect to the problem which requires students to relate the decimal numbers in the expressions to key physical concepts.
Show without recourse to any calculating aid that 7^{1/2} + 7^{1/3} + 7^{1/4} < 7 and 4^{1/2} + 4^{1/3} + 4^{1/4} > 4 . Sketch the graph of f(x) = x^{1/2} + x^{1/3} + x^{1/4} -x