Question

help me pleaseeeeeee!the result is (rational/irrational) because it (cannot/can) be written as the ratio of two integers and it’s decimal expansion (does/does not) terminate or repeat

Answer 1

$4\sqrt[]{3}\times2\sqrt[]{27}$

To multiply the above numbers, here are the steps:

1. Multiply the whole number and the radicands.

$\begin{gathered} 4\times2=8 \\ \sqrt[]{3}\times\sqrt[]{27}=\sqrt[]{81} \end{gathered}$

2. Get the square root of 81.

$\sqrt[]{81}=9$

3. Multiply the answer in #2 to the product of the whole numbers.

$8\times9=72$

Therefore, the product of 4√3 and 2√27 is 72.

The result is rational because it can be written as the ratio of two integers and its decimal expansion does terminate or repeat.