Question

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

Answer 1

First is 21. Square root of 3 squared is actually 3

Second 5. Same with 5

Third 12

Forth is irrational

So first 3 are the answers

Answer 2

the first 3

using the law of radicals

•
`√(a)` ×
`√(b)` ⇔
`√(ab)`

•
`√(a)` ×
`√(a)` = a

7
`√(3)`
`√(3)` = 7 × 3 = 21 ← rational

`√(5)` ×
`√(5)` = 5 ← rational

2
`√(9)` ×
`√(4)` = 2 ×
`√(36)` = 2 × 6 = 12 ← rational

`√(3)` ×
`√(16)` = 4
`√(3)` ← irrational