Find the cube root of the following rational numbers: 0.001728 - Vidyadip

Question

Find the cube root of the following rational numbers:
0.001728

✓

Answer

We have:
$0.001728=\frac{1728}{1000000}$
$\therefore\sqrt[3]{0.0001728}$
$=\sqrt[]{\frac{1828}{1000000}}$
$={\frac{\sqrt[3]{1828}}{\sqrt[3]{1000000}}}$
Now
On factorising 1728 into prime factors, we get:
1728 = 2 × 2 × 2 × 2 × 2 × 2 × 3 × 3 × 3
On grouping the factors in triples of equal factors, we get:
1728 = {2 × 2 × 2} × {2 × 2 × 2} × {3 × 3 × 3}
Now, taking one factor from each triple, we get:
$\sqrt[3]{1728}=2\times2\times3=12$
Also
$\sqrt[3]{1000000}$
$\sqrt[3]{100\times100\times100}=100$
$\therefore\sqrt[3]{0.001728}$
$={\frac{\sqrt[3]{1828}}{\sqrt[3]{1000000}}}$
$\frac{12}{100}=0.12$

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