Question

Select all numbers that will produce an IRRATIONAL number when multiplied by 25–√
.

(Select all that apply.)

(2 points)
Responses

32–√

3 square root of 2

−5–√

negative square root of 5

45√

the fraction with numerator 4 and denominator square root of 5

1+5–√

1 plus square root of 5

125−−−√

Answer 1

√25 = 5 (a rational number). A nonzero rational times an irrational is always irrational, and a rational times a rational is rational. So the products will be irrational exactly for the choices that are irrational themselves:

Select: √32, 3√2, −√5 (negative square root of 5), √45, 4/√5, 1+√5, and √125.