Question

Given:

A = √3
B = 2√3
C = √25
D=√16
Which expressions result in a rational number? Select all that apply.
a) А+В
b) C+D
c) A+D
d) A.B
e) B.D
f) C.D
g) A.A

Answer 1

To determine which expressions result in a rational number, we need to check if the square root in each expression simplifies to a rational number. The expressions that result in a rational number are: C + D, A.B, B.D, C.D, and A.A.

Step-by-step explanation:

To determine which expressions result in a rational number, we need to check if the square root in each expression simplifies to a rational number. A rational number is a number that can be expressed as a fraction, where both the numerator and denominator are integers.

1. A + B: (√3) + (2√3) = 3√3, which is not a rational number.
2. C + D: (√25) + (√16) = 5 + 4 = 9, which is a rational number.
3. A + D: (√3) + (√16) = √3 + 4, which is not a rational number.
4. A.B: (√3)(2√3) = 6, which is a rational number.
5. B.D: (2√3)(√16) = 2(4) = 8, which is a rational number.
6. C.D: (√25)(√16) = 5(4) = 20, which is a rational number.
7. A.A: (√3)(√3) = 3, which is a rational number.

Therefore, the expressions that result in a rational number are: C + D, A.B, B.D, C.D, and A.A.