Question

Which statement is true?

A. The product 3 * √12 is rational because √12 can be expressed as a tion.
B. The product √3 * √12 is rational because the product of two irrational numbers cannot be expressed as a tion.
C. The product √3.12 is irrational because √3.12 can be expressed as a tion.
D. The product √3 * √12 is irrational because the product of two irrational numbers cannot be expressed as a tion.

Answer 1

The product of √3 * √12 is irrational because it cannot be expressed as a ratio of two integers.

Step-by-step explanation:

The statement that is true is option D: The product √3 * √12 is irrational because the product of two irrational numbers cannot be expressed as a ratio.

To see why, let's consider the product: √3 * √12.

1. First, simplify the radicals: √3 = 1.732 and √12 = 3.464.
2. Next, multiply the simplified values: 1.732 * 3.464 = 5.999168.
3. The result, 5.999168, is not a rational number because it cannot be expressed as a ratio of two integers.

Therefore, the product √3 * √12 is irrational.