Question

Is the number rational or irrational?
A) -3√8
B) 2√3 - √27

Answer 1

Both numbers, -3√8 and 2√3 - √27, are irrational once simplified.

Step-by-step explanation:

To determine if the numbers -3√8 and 2√3 - √27 are rational or irrational, we need to simplify them first.

Let's start with A) -3√8. We can rewrite -3√8 as -3√(2³), which simplifies to -3×2√2, or -6√2. Since √2 is an irrational number, the product of a rational (-6) and an irrational (√2) number is also irrational.

Now for B) 2√3 - √27. We know that √27 can be rewritten as √(3³) which simplifies to 3√3. Subtracting this from 2√3, we get -√3, an irrational number since √3 is irrational.

So both A) -3√8 and B) 2√3 - √27 are irrational numbers.