Question

Which of the following numbers are cubes of negative integers? [4 MARKS]

(a) -64 (b) -2197 (c) -1056 (d) -3888

Answer 1

Application: 1 Mark each

$\left(a\right)64=2\times 2\times 2\times 2\times 2\times 2$

$\sqrt[3]{364}=\sqrt[3]{32\times 2\times 2\times 2\times 2\times 2}=2\times 2=4$

$\sqrt[3]{3-64}=-\sqrt[3]{364}=-4$

$\therefore$ -64 is a cube of -4, a negative integer.

$\left(b\right)2197=13\times 13\times 13$

$\sqrt[3]{32197}=\sqrt[3]{313\times 13\times 13=13}$

$\sqrt[3]{3-2197}=-\sqrt[3]{32197}=-13$

$\therefore$ -2197 is a cube of -13, a negative integer.

$\left(c\right)1056=13\times 13\times 13$

$\sqrt[3]{32197}=\sqrt[3]{32\times 2\times 2\times 2\times 2\times 3\times 11}$

In the above factorisation $2\times 3\times 3\times 11\times 11$ remains after grouping in triplets. Therefore, 1056 is not a perfect cube.

Hence -1056 is not a cube of negative integer.

$\left(d\right)3888=2\times 2\times 2\times 2\times 3\times 3\times 3\times 3\times 3$

In the above factorisation $2\times 3\times 3$ remains after grouping in triplets. Therefore, 3888 is not a perfect cube.

Hence -3888 is not a cube of negative integer.