Question

Find the rational number whose cube is 0.001728

Answer 1

Answer:

0.001728 is the cube of $\frac{3}{25}$

Step-by-step explanation:

0.001728 = $\frac{1728}{1000000}$

break down each using LCD

1728 / 2 = 864

864 / 2 = 432

432 / 2 = 216

216 / 2 = 108

108 / 2 = 54

54 / 3 = 27

27 / 3 = 9

9 / 3 = 3

3 / 3 = 1

1000000 / 2 = 500000

500000 / 2 = 250000

250000 / 2 = 125000

125000 / 2 = 62500

62500 / 2 = 31250

31250 / 5 = 15625

15625 / 5 =3125

3125 / 5 =625

625 /2 = 125

125 / 5 =25

25 / 5 = 5

5 / 5 = 1

*don't forget to add another 2 for each group*

$\frac{1728}{1000000}$ = $\frac{2 * 2 * 2 * 2 * 2 * 2 * 3 * 3 * 3}{2 * 2 * 2 * 2 * 2 * 2 * 5 * 5 * 5 * 5 * 5 * 5}$  

= $\frac{3 * 3 * 3}{5 * 5 * 5 * 5 * 5 * 5}$

= $({\frac{3x^{3} }{5x^{3} * 5x^{3} })^{3}$

= $\sqrt[3]{\frac{1728}{1000000} } = (\frac{3}{5 * 5} )^{3}$

=$\sqrt[3]{\frac{1728}{1000000} } = \frac{3}{5 * 5}$

= $\sqrt[3]{0.001728} = \frac{3}{25}$

Answer 2

This is the cube of 3/25