Stage: 5 Challenge Level: 
Evaluate without a calculator:
$(5\sqrt 2 + 7)^{{1\over 3}} - (5\sqrt 2 - 7)^{{1\over 3}}.$
Modulus arithmetic. Complex roots of equations in conjugate pairs. Index notation/Indices. Complex numbers. Argand diagram. Quadratic equations. Long problems. Surds. Pythagoras' theorem. Powers & roots.
Published February 1998.
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