Find the value of ^@\sqrt[3]{ -1728}^@ . | Math Question and Answer | Edugain Singapore

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Find the value of $\sqrt[3]{ -1728}$ .

Answer:

$-12$

Step by Step Explanation:

Let's first find all prime factors of $1728$ .
$1728 = 2 \times 2 \times 2 \times 2 \times 2 \times 2 \times 3 \times 3 \times 3$
Now, $\sqrt[3]{ -1728}$
$= -1 × \sqrt[3]{ 2 \times 2 \times 2 \times 2 \times 2 \times 2 \times 3 \times 3 \times 3 } \\ = -1 × \sqrt[3]{ 2^3 \times 2^3 \times 3^3 } \\ = -1 × 2 × 2 × 3 \\ = -12$

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