The product of a non-zero rational number and an irrational number is always an irrational number. Here's why:

Step 1: Understand the terms. A rational number is any number that can be expressed as the quotient or fraction p/q of two integers, with the denominator q not equal to zero. An irrational number cannot be expressed as a ratio between two numbers and it does not repeat or terminate.

Step 2: Consider an example. Let's take a non-zero rational number, like 2, and an irrational number, like the square root of 2.

Step 3: Multiply these numbers together. 2 * √2 = 2√2.

Step 4: Check if the result is rational or irrational. In this case, 2√2 is still an irrational number because it cannot be expressed as a ratio of two integers.

So, the product of a non-zero rational number and an irrational number is always an irrational number.

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The product of a non-zero rational number and an irrational number is always an irrational number. Here's why:

Step 1: Understand the terms. A rational number is any number that can be expressed as the quotient or fraction p/q of two integers, with the denominator q not equal to zero. An irrational number cannot be expressed as a ratio between two numbers and it does not repeat or terminate.

Step 2: Consider an example. Let's take a non-zero rational number, like 2, and an irrational number, like the square root of 2.

Step 3: Multiply these numbers together. 2 * √2 = 2√2.

Step 4: Check if the result is rational or irrational. In this case, 2√2 is still an irrational number because it cannot be expressed as a ratio of two integers.

So, the product of a non-zero rational number and an irrational number is always an irrational number.

Knowee AI · Accepted Answer

The product of a non-zero rational number and an irrational number is always an irrational number. Here's why:

Step 1: Understand the terms. A rational number is any number that can be expressed as the quotient or fraction p/q of two integers, with the denominator q not equal to zero. An irrational number cannot be expressed as a ratio between two numbers and it does not repeat or terminate.

Step 2: Consider an example. Let's take a non-zero rational number, like 2, and an irrational number, like the square root of 2.

Step 3: Multiply these numbers together. 2 * √2 = 2√2.

Step 4: Check if the result is rational or irrational. In this case, 2√2 is still an irrational number because it cannot be expressed as a ratio of two integers.

So, the product of a non-zero rational number and an irrational number is always an irrational number.

The product of a non-zero rational and an irrational number i

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