Question

Select all numbers that will produce an IRRATIONAL number when multiplied by 2sqrt5
.

(Select all that apply.)

(2 points)
Responses

3sqrt2

3 square root of 2

−sqrt5

negative square root of 5

4/sqrt5

the fraction with numerator 4 and denominator square root of 5

1 + sqrt5

1 plus square root of 5

sqrt125

Answer 1

Selected: 3√2 and 1 + √5.

Reasoning:
- 2√5 * 3√2 = 6√10 (√10 irrational) → irrational.
- 2√5 * (1 + √5) = 10 + 2√5 (sum includes nonzero irrational term) → irrational.

Not selected:
- 2√5 * (−√5) = −10 → rational.
- 2√5 * (4/√5) = 8 → rational.
- 2√5 * √125 = 2√5 * 5√5 = 50 → rational.