Question

Which of the following results in a sum or a product that is rational? Choose all that apply.

A. pi times six
B. StartRoot 3 EndRoot plus StartRoot 5 EndRoot
C. 4 + 6
D. 3 point ModifyingAbove 15 with bar times 4.6
E. StartRoot 64 EndRoot times StartRoot 25 EndRoot

Answer 1

The correct options are C, D and E.

Explanation:

Consider the provided information.

We need to find the results in a sum or a product that is rational.

Consider the provided options.

Option A) π × 6

π × 6 = 18.8495559215...

The decimal expansion of

the above number is neither terminate nor

periodic.

Hence the option is incorrect.

Option B) √3 + √5

√3+√5=1.73205080757..+2.2360679775..=3.96811878507....

The decimal expansion of

the above number is neither terminate nor

periodic.

Hence the option is incorrect.

Option C) 4 + 6

4+6=10 which is a rational number.

The sum of two rational numbers is rational.

Hence the option is correct.

Option D)
`3.\overline{15}` × 4.6

`3.\overline{15}` is a rational number because the decimal expansion is repeating and 4.6 is a rational number because the decimal expansion is terminating.

The product of two rational numbers is rational.

Hence the option is correct.

Option E) √64 × √25

This can be written as: 8 × 5 (because √64 =8 and √25=5)

8 and 5 are rational numbers.

The product of two rational numbers is rational.

Hence the option is correct.

Thus, the correct options are C, D and E.

Answer 2

Let's investigate by defining what a rational number is. A rational number is a real number that can be expressed as whole numbers, integers, and fractions.

A. π is a irrational number to start. So, this is not the answer.
B. √3 + √5 = 9.96811... This is not the answer.
C. 4 + 6 = 10. Since it is a whole number, this is the answer.
D. 3.15151515,,, is an irrational number to start. So, this is not the answer.
E. (√64)(√25) = (8)(5) = 40. This is rational

Hence, the answers are C and E.