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

The expression that simplify to a rational answer are:

`√(5) *√(5)`

`2√(9) *√(4)`

`7√(3) *√(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.
`√(5) *√(5)=√(5*5) =√(5^2) =5`

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

2.
`√(3) *√(16) =√(3*16) =√(48)=4√(3)`

Since
`4√(3)` is irrational, our expression doesn't simplifies to a rational answer.

3.
`2√(9) *√(4) =2√(9*4)=2 √(36) =2√(6^2) =2*6=12`

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

4.
`7√(3) *√(3) =7√(3*3) =7√(3^2) =7*3=21`

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