TSR Wiki > Study Help > Subjects and Revision > Mathematics > STEP > STEP II 2007 question 1 solution
i)
a)
So
By long division.
b) Take k=-4. Then:
ii)
Pick k=29. Then
Solution by SsEe.
![\left( 1 + \frac{29}{1000} \right)^{\frac{1}{3}} = \left( \frac{1029}{1000} \right)^{\frac{1}{3}} = \left( \frac{3 \times 343}{1000} \right)^{\frac{1}{3}} = \frac{7}{10} \sqrt[3]{3}](http://www.thestudentroom.co.uk/latexrender/pictures/16/1620ebaeff00d5a141391c3e7688319f.png "\left( 1 + \frac{29}{1000} \right)^{\frac{1}{3}} = \left( \frac{1029}{1000} \right)^{\frac{1}{3}} = \left( \frac{3 \times 343}{1000} \right)^{\frac{1}{3}} = \frac{7}{10} \sqrt[3]{3}")
![\sqrt[3]{3} \approx \frac{3000 + 29}{3000 \times \left( \frac{7}{10} \right)} = \frac{3029}{2100}](http://www.thestudentroom.co.uk/latexrender/pictures/49/49092785c0f66dfea0268da5016e0b00.png "\sqrt[3]{3} \approx \frac{3000 + 29}{3000 \times \left( \frac{7}{10} \right)} = \frac{3029}{2100}")
