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Which expressions simplify to a rational answer?

Select each correct answer.

Which expressions simplify to a rational answer? Select each correct answer.-example-1
User Pmorken
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2 Answers

4 votes
1. 5 (yes)
2. 4 \sqrt{3} (no)
3. 12 (yes)
4. 21 (yes)
User Pawan Dongol
by
8.1k points
0 votes

Answer

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.

User Rickstar
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