Question

Which expressions simplify to a rational answer? Select each correct answer.

Answer 1

1. 5 (yes)
2.  4 \sqrt{3} (no)
3. 12 (yes)
4. 21 (yes)

Answer 2

Answer

The expression that simplify to a rational answer are:

$\sqrt{5} *\sqrt{5}$

$2\sqrt{9} *\sqrt{4}$

$7\sqrt{3} *\sqrt{3}$

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. $\sqrt{5} *\sqrt{5}=\sqrt{5*5} =\sqrt{5^2} =5$

Since 5 is rational, our expression simplifies to a rational answer.

2. $\sqrt{3} *\sqrt{16} =\sqrt{3*16} =\sqrt{48}=4\sqrt{3}$

Since $4\sqrt{3}$ is irrational, our expression doesn't simplifies to a rational answer.

3. $2\sqrt{9} *\sqrt{4} =2\sqrt{9*4}=2 \sqrt{36} =2\sqrt{6^2} =2*6=12$

Since 12 is rational, our expression simplifies to a rational answer.

4. $7\sqrt{3} *\sqrt{3} =7\sqrt{3*3} =7\sqrt{3^2} =7*3=21$

Since 21 is rational, our expression simplifies to a rational answer.