Given that the product of two rational numbers is rational, and…

Question 6 of 26beginner🔧 ApplyShort Answer1 mark

Given that the product of two rational numbers is rational, and suppose $a$ and $b$ are rationals, what can you conclude about $ab$ ?

Correct Answer

Since $a$ and $b$ are both rational numbers, and it is given that the product of two rational numbers is rational, we can conclude that $ab$ is a rational number.

Exercise: EXERCISE A1.2 | Q: 2 | (Page 6)

For More Understanding

Explanation

The question directly applies the given premise. The statement explicitly provides that the product of two rational numbers is rational. Since both $a$ and $b$ are given to be rational numbers, their product $ab$ must necessarily be rational by direct application of this given fact.

Solution Steps

Step 1: Identify that $a$ and $b$ are rational numbers (given in question).
Step 2: Apply the given statement that the product of two rational numbers is rational.
Step 3: Conclude that $ab$ is a rational number.

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