Answer
The expression that simplify to a rational answer are:
[tex]\sqrt{5} *\sqrt{5}[/tex]
[tex]2\sqrt{9} *\sqrt{4}[/tex]
[tex]7\sqrt{3} *\sqrt{3}[/tex]
Explanation
Remember that to multiply radicals/roots of the same index, we just need to multiply the radicans (the numbers inside the radical/root) and simplify. Let's simplify each of our expressions.
1. [tex]\sqrt{5} *\sqrt{5}=\sqrt{5*5} =\sqrt{5^2} =5[/tex]
Since 5 is rational, our expression simplifies to a rational answer.
2. [tex]\sqrt{3} *\sqrt{16} =\sqrt{3*16} =\sqrt{48}=4\sqrt{3}[/tex]
Since [tex]4\sqrt{3}[/tex] is irrational, our expression doesn't simplifies to a rational answer.
3. [tex]2\sqrt{9} *\sqrt{4} =2\sqrt{9*4}=2 \sqrt{36} =2\sqrt{6^2} =2*6=12[/tex]
Since 12 is rational, our expression simplifies to a rational answer.
4. [tex]7\sqrt{3} *\sqrt{3} =7\sqrt{3*3} =7\sqrt{3^2} =7*3=21[/tex]
Since 21 is rational, our expression simplifies to a rational answer.
