Which expressions below equal a rational number? Choose all that apply.

the first one : 4/5 + 3/8

the third one : 7×sqrt(5) - sqrt(245)

the 4th one : 4×sqrt(7) × 2×sqrt(7)

Step-by-step explanation:

per definition, the set of rational numbers is the set of all integers and fractions.

the first answer is simply a prime example of fraction operation, and the result is therefore a fraction again.

the 3rd answer delivers 0, because

sqrt(245) = sqrt(49×5) = 7×sqrt(5). this is a rare occasion where an operation with a non-rational number still delivers a rational result.

the 4th answer squares the square root of 7 creating 7, which creates overall an integer and therefore rational result.

the other options contain at least one number that is not rational and will not be converted or neutralized by the operation.

and the sum and product of a rational with a non-rational number is always non-rational.

sqrt(100) + sqrt(5) = 10 + sqrt(5).

as 5 is not a square number, its square root contains an infinite number of digits after the decimal point without any repeating pattern. this is a real number, not a rational number.

pi is per definition not rational (same thing as for sqrt(5) : infinite number of digits after the decimal point without any repeating pattern).