Which of the following rational numbers is not between 3–√ and 6–√ ? show you r work

Answer 1

To determine which rational number is not between $\sqrt{3}$ and $\sqrt{6}$, we first need to calculate the approximate values of these square roots.

1. Calculate $\sqrt{3}$: $$\sqrt{3}\approx 1.732$$

2. Calculate $\sqrt{6}$: $$\sqrt{6}\approx 2.449$$

Now we know that $\sqrt{3}\approx 1.732$ and $\sqrt{6}\approx 2.449$. Therefore, we need to identify rational numbers that lie between these two values.

Any rational number $x$ that satisfies: $$\sqrt{3}<x<\sqrt{6}$$ or $$1.732<x<2.449$$ is considered to be between $\sqrt{3}$ and $\sqrt{6}$.

Let's check some potential rational numbers:

• Number 1: $1.8$

  • Since $1.732<1.8<2.449$, it is between $\sqrt{3}$ and $\sqrt{6}$.

• Number 2: $2.3$

  • Since $1.732<2.3<2.449$, it is also between $\sqrt{3}$ and $\sqrt{6}$.

• Number 3: $2.5$

  • Since $2.5>2.449$, it is not between $\sqrt{3}$ and $\sqrt{6}$.

• Number 4: $2$

  • Since $1.732<2<2.449$, it is between $\sqrt{3}$ and $\sqrt{6}$.

To sum up, among the rational numbers we looked at, $2.5$ is the one that is not between $\sqrt{3}$ and $\sqrt{6}$.