Question

Which expressions represent rational numbers? Check all that apply.

Answer 1

Question:

a. StartRoot 6 EndRoot + StartRoot 9 EndRoot

b. StartRoot 64 EndRoot + StartFraction 6 Over 11 EndFraction

c. StartRoot 36 EndRoot + StartRoot 21 EndRoot

d. StartRoot 16 EndRoot + StartRoot 169 EndRoot

e. 17.ModifyingAbove 43 with bar + StartRoot 49 EndRoot

f. StartRoot 44 EndRoot + StartRoot 25 EndRoot

Answer:

The correct options are

b. d. and e.

Step-by-step explanation:

A rational number, Q can be expressed as a fraction or ratio of two integers such as a/b where b is not equal to  0

Therefore, among the options, we have;

a) √6 is not a rational number

b) Here we have √64 + 6/11 = 8 + 6/11 =94/11  is a rational number

c) √21 is not a rational number

d) √16 + √169 = 4 + 13 = 17

e)  17.43 + √49 where .43 is a repeating decimal gives

17.43 +7 = 24.43 where .43 is repeating yields a rational number

f) √44 is not a rational number

Answer 2

Answer:

a and e

Step-by-step explanation:

As we know that: repeating number is rational

a. StartRoot 6 EndRoot + StartRoot 9 EndRoot

= $\sqrt{6} +\sqrt{9}$

Sum is not rational

b. StartRoot 64 EndRoot + StartFraction 6 Over 11 EndFraction

= $\sqrt{64} +\frac{6}{11}$

Sum is rational because $\frac{6}{11}$  is rational

c. StartRoot 16 EndRoot + StartRoot 169 EndRoot

= $\sqrt{16} +\sqrt{169}$

= 4+13=17

Sum is not rational

d. StartRoot 44 EndRoot + StartRoot 25 EndRoot

=$\sqrt{44} + \sqrt{25}$

Sum is not rational

e. ModifyingAbove 43 with bar + StartRoot 49 EndRoot

Sum is rational because ModifyingAbove 43 with bar is  rational