Respuesta :
Answer:
A. the sum of two irrational numbers
B. the product of two irrational numbers
Step-by-step explanation:
A. The sum of two rational number is sometimes a rational number.
For Example: (2 + √3) + (5 -√3) = 8 which is a rational number.
B. The product of two irrational number can be a rational number but it is not always true.
For Example: (8 + √3) × (8 -√3) = 8² - 3 = 64 - 3 = 61
C. The sum of rational and irrational number is always a rational number.
For Example: 2 + √5 which is an irrational number.
D. The product of rational and irrational number is always an irrational number.
For Example: 8 × (2 + √3) = 16 + 8√3 which is an irrational number.
Further, Rational Number is the number in the form [tex]\frac{p}{q}[/tex], where q≠0.
Example: [tex]\frac{2}{9}, \frac{-1}{267}, \frac{875}{2}, 3, etc.[/tex]
The decimal which is non-terminating, non-repeating decimal expansion and thus it can't be written in the form of simple fraction is called irrational number.
Example: √5, π, 27.458978445...., etc.
The possibility of obtaining a rational number from the option is ;
• Sum of two irrational numbers .
• Product of two irrational numbers .
Rational numbers are real numbers which can be expressed in the form, a/b ; where, b ≠ 0.
Irrational numbers are real numbers which cannot be expressed in the form a/b. For instance, √3, 3.14236..., √3 + 5
The sum of two irrational numbers could sometimes give a rational number.
Let :
A = √3 + 5 ; B = 5 - √3
A + B = (√3 + 5) + (5 - √3)
A + B = √3 + 5 + 5 - √3
A + B = √3 - √3 + 5 + 5
A + B = 10 (Rational number)
The product of two irrational numbers :
A = √3 + 5 ; B = 5 - √3
A × B = (√3 + 5) × (5 - √3)
A × B = 5√3 - 3 + 25 - 5√3
A × B = 5√3 - 5√3 - 3 + 25
A × B = 22 (Rational number)
The sum of a rational and an irrational number :
Rational = A = 2 ;
Irrational, = B = √3
A + B = 2 + √3 (Irrational number)
The product of rational and irrational number :
Rational = A = 2 ;
Irrational, = B = √3
A × B = 2 × √3 = 2√3 (Irrational number)
Learn more : https://brainly.com/question/12542057
