Which statement best explains why the number 5√2 is irrational?

Question

A. The result of squaring 5√2 is not a rational number.

B. The number 5 is not divisible by 2.

C. The product of a positive integer and an irrational number is irrational.

D. The product of an odd number and the square root of an even number is irrational.

Answer 1

The best statement that explains why the number \( 5\sqrt{2} \) is irrational is:

C. The product of a positive integer and an irrational number is irrational.

This is because \( \sqrt{2} \) is irrational, and multiplying it by the rational number 5 results in an irrational number \( 5\sqrt{2} \).