Question

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

Answer 1

All but the first simplify to something rational.

• $\sqrt{3}\cdot\sqrt{16}=4\sqrt{3}\qquad\text{irrational}$
• $2\sqrt{9}\cdot\sqrt{4}=2\cdot 3\cdot 2=12$
• $7\sqrt{3}\cdot\sqrt{3}=7\cdot 3=21$
• $\sqrt{5}\cdot\sqrt{5}=5$

Answer 2

a rational number is a number that can be written in form a/b where a and b are integers (integers are like -5,-4,-3,-2,-1,0,1,2,3,4, etc)

remember that (√a)(√b)=√(ab)

and √(a^2)=a

do each

√3 · √16=√3·√(4^2)=√3·4=4√3 which is irrational

2√9·√4=2√(3^2)·√(2^2)=2(3)·2=6·2=12 which is rational

7√3·√3=7√(3·3)=7√(3^2)=7(3)=21 which is rational

√5·√5=√(5·5)=√(5^2)=5 which is rational

rational expressions:

2√9·√4

7√3·√4

√5·√5

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