Find the cube root of each of the following rational numbers:
(i) $0.001728$
(ii) $0.003375$
(iii) $0.001$
(iv) $1.331$

To find: 

We have to find the cube root of the given rational numbers.

Solution:

(i) $\sqrt[3]{0.001728}=\sqrt[3]{\frac{1728}{1000000}}$

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

$=\frac{\sqrt[3]{2 \times 2 \times 2 \times 2 \times 2 \times 2 \times 3 \times 3 \times 3}}{\sqrt[3]{10 \times 10 \times 10 \times 10 \times 10 \times 10}}$

$=\frac{\sqrt[3]{2^{3} \times 2^{3} \times 3^{3}}}{\sqrt[3]{10^{3} \times 10^{3}}}$

$=\frac{2 \times 2 \times 3}{10 \times 10}$

$=\frac{12}{100}$

$=0.12$

(ii) $\sqrt[3]{0.003375}=\sqrt[3]{\frac{3375}{1000000}}$

$=\frac{\sqrt[3]{3375}}{\sqrt[3]{1000000}}$

$=\frac{\sqrt[3]{3 \times 3 \times 3 \times 5 \times 5 \times 5}}{\sqrt[3]{10 \times 10 \times 10 \times 10 \times 10 \times 10}}$

$=\frac{\sqrt[3]{3^{3} \times 5^{3}}}{\sqrt[3]{10^{3} \times 10^{3}}}$

$=\frac{3 \times 5}{10 \times 10}$

$=\frac{15}{100}$

$=0.15$

(iii) $\sqrt[3]{0.001}=\sqrt[3]{\frac{1}{1000}}$

$=\frac{\sqrt[3]{1}}{\sqrt[3]{1000}}$

$=\frac{\sqrt[3]{1 \times 1 \times 1}}{\sqrt[3]{10 \times 10 \times 10}}$

$=\frac{1}{\sqrt[3]{10^{3}}}$

$=\frac{1}{10}$

$=0.1$

(iv) $\sqrt[3]{1.331}=\sqrt[3]{\frac{1331}{1000}}$

$=\frac{\sqrt[3]{1331}}{\sqrt[3]{1000}}$

$=\frac{\sqrt[3]{11 \times 11 \times 11}}{\sqrt[3]{10 \times 10 \times 10}}$

$=\frac{\sqrt[3]{11^{3}}}{\sqrt[3]{10^{3}}}$

$=\frac{11}{10}$

$=1.1$

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Updated on: 10-Oct-2022

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