We have 23, #160;34 #160;and #160;43. The orders of 23, #160;34 #160;and #160;43 nbsp; are 3, 4 and 3. The LCM of 3, 4 and 3 is 12. So, we will m ...

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Real Numbers

iii 23, 34, 4...

Question

(iii) $\sqrt[3]{2}, \sqrt[4]{3}, \sqrt[3]{4}$

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Solution

We have $\sqrt[3]{2}, \sqrt[4]{3} and \sqrt[3]{4}$ .
The orders of $\sqrt[3]{2}, \sqrt[4]{3} and \sqrt[3]{4}$ are 3, 4 and 3.

The LCM of 3, 4 and 3 is 12.
So, we will make the order of all the surds 12.

$\sqrt[3]{2} = \sqrt[3 \times 4]{2^{4}} = \sqrt[12]{16} \sqrt[4]{3} = \sqrt[4 \times 3]{3^{3}} = \sqrt[12]{27} and \sqrt[3]{4} = \sqrt[3 \times 4]{4^{4}} = \sqrt[12]{256}$

Hence, the order is same.
Since 16 < 27 < 256, $\sqrt[3]{2} < \sqrt[4]{3} < \sqrt[3]{4}$ .

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