The product of 4√6 and 3√24 is:

Correct option is C

Given:

We need to find the product of $$4\sqrt{6}$$​ and $$3\sqrt{24}$$​ and determine its nature.

Concept Used:

The product of two square roots can be simplified using:
​$$\sqrt{a} \times \sqrt{b} = \sqrt{a \times b}$$​​

Solution:
​$$4\sqrt{6} \times 3\sqrt{24}\\\ \\= (4 \times 3) \times (\sqrt{6} \times \sqrt{24}) = 12\times \sqrt{6\times24}\\= 12\times \sqrt{144}\\= 12\times12\\= 144$$​​

Since 144 is a whole number, it is a rational number.

Then the correct option is C. The product is a rational number.