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

• $\sqrt{a}$ × $\sqrt{b}$ ⇔ $\sqrt{ab}$

• $\sqrt{a}$ × $\sqrt{a}$ = a

7$\sqrt{3}$ $\sqrt{3}$ = 7 × 3 = 21 ← rational

$\sqrt{5}$ × $\sqrt{5}$ = 5 ← rational

2$\sqrt{9}$ × $\sqrt{4}$ = 2 × $\sqrt{36}$ = 2 × 6 = 12 ← rational

$\sqrt{3}$ × $\sqrt{16}$ = 4$\sqrt{3}$ ← irrational