Final answer:
The product 5.15 x 6√7 is irrational because it is the multiplication of a rational number (5.15) and an irrational number (6√7).
Step-by-step explanation:
The question asks whether 5.15 x 6√7 is rational or irrational. To determine this, we need to understand the nature of the numbers involved. The number 5.15 is a decimal and since it is terminating, it is rational. However, the √7 represents the square root of 7, which is an irrational number because it cannot be expressed as a fraction of two integers. Additionally, according to mathematical properties, the square root can also be expressed as a fractional power of a number, for example, x² = √x. Therefore, multiplying a rational number by an irrational number results in an irrational number. This means that 5.15 x 6√7 is an irrational number because the product of a rational and an irrational number is always irrational.