Express $2744$ as a product of its prime factors, giving your answer in index notation. Hence, fin

Question

Express $2744$ as a product of its prime factors, giving your answer in index notation. Hence, find $\sqrt[3]{2744}$ without the use of a calculator. Given that $2744k$ is a perfect square, write down the smallest possible positive integer value of $k$.

Accepted Answer

(a) $2^3\times7^3$ (b) $14$ (c) $14$

Prime Factorisation, Cube Roots, and Perfect Square Conditions

Prime Factorisation, Cube Roots, and Perfect Square Conditions

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