Given:
A = √3
B = 2√3
C = √25
D = √16
Which expressions result in a rational number? Select all that apply.
A) A+B
B) C+D
C) A+D
D) A *B
E) B*D
F) C*D
G) A* A
Justify your answers
A rational number can be expressed as a fraction of two integers.
A) A+B: √3 + 2√3 = 3√3, which is irrational because the square root of 3 is irrational.
B) C+D: √25 + √16 = 5 + 4 = 9, which is a rational number because it can be expressed as the fraction 9/1.
C) A+D: √3 + √16 = √3 + 4, which is irrational because the square root of 3 is irrational.
D) A *B: √3 * 2√3 = 6, which is a rational number because it can be expressed as the fraction 6/1.
E) B*D: 2√3 * √16 = 2 * 4 = 8, which is a rational number because it can be expressed as the fraction 8/1.
F) C*D: √25 * √16 = 5 * 4 = 20, which is a rational number because it can be expressed as the fraction 20/1.
G) A * A: √3 * √3 = 3, which is a rational number because it can be expressed as the fraction 3/1.
The expressions that result in a rational number are B), D), E), F), and G).