Example problems for cube numbers — lesson. Mathematics State Board, Class 8.

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1. Find the cube of

$21$ .

Solution:

If you multiply a number by itself and then by itself again (thrice), the result is a cube number.

$21 = 21 \times 21 \times 21 = 9261$

Therefore, the cube of

$21$ is

$9261$ .

2. Is

$625$ is a perfect cube? If not, make it as a perfect cube by the multiplication of smallest number.

Solution:

$\begin{array}{l} \underline{5 | 625} \\ \underline{5 | 125} \\ \underline{5 | 25} \\ \underline{5 | 5} \\ | 1 \end{array}$

Group the factors in pair of three numbers.

$125 = (5 \times 5 \times 5) \times 5$

Here, factor

$5$ is leftover.

So,

$625$ is not a perfect cube.

To make it as a perfect cube, we need two more

$5$ 's.

So, multiply the given number by two

$5$ 's.

$625 \times 5 \times 5 = 15625$

Therefore,

$15625$ is a perfect cube.

3. Is

$243$ is a perfect cube? If not, find the smallest number to divide

$243$ to make it as a perfect cube.

Solution:

$243 = (3 \times 3 \times 3) \times 3 \times 3$

Here, factor

$3 \times 3 = 9$ is leftover while grouping.

So,

$243$ is not a perfect cube.

To make it as a perfect cube, divide the given number by the leftover factor

$9$ .

$\frac{243}{9} = 27$

Therefore,

$9$ is the smallest number to divide

$243$ , and the obtained perfect square is

$27$ .

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3. Example problems for cube numbers

Theory: