Final answer:
The student's question asking what number can be multiplied by √7 to get a rational number has two correct answers, 0 and √7. Multiplying √7 by 0 results in 0, and multiplying it by itself results in 7; both are rational numbers.
Step-by-step explanation:
The student asked: What number can you multiply by √7 to get a rational number? The provided options are √-7, 0, 7, √7, and they have to select each correct answer. First, we need to understand that a rational number is a number that can be expressed as a fraction where both the numerator and the denominator are integers. The square root of 7, √7, is an irrational number because it cannot be precisely written as a fraction.
To obtain a rational number by multiplying √7, we need to multiply it by a number that will eliminate the irrational part. Multiplying √7 by 0 will give us 0, which is indeed a rational number. Multiplying √7 by itself, √7 * √7, will give us 7, which is also a rational number.
The correct answers are thus:
It is important to eliminate terms wherever possible to simplify the algebra and then to check the answer to see if it is reasonable. In this case, both of the selected options yield rational numbers when multiplied by √7, confirming that the choices are correct.