Question

without using a calculator, determine which expression has the value shown by the point on the number line below.$sqrt{24}$$sqrt{14}$$sqrt{2}$$sqrt{6}$

Explanation:

Step1: Locate point on number line

The point is between 4 and 5, so $4 < x < 5$.

Step2: Square all parts of inequality

$$4^2 < x^2 < 5^2$$
$$16 < x^2 < 25$$

Step3: Match to square root values

We need an expression where the radicand is between 16 and 25.

• $\sqrt{24}$: $24$ is between $16$ and $25$
• $\sqrt{14}$: $14 < 16$, so $\sqrt{14}<4$
• $\sqrt{2}$: $2 < 16$, so $\sqrt{2}<4$
• $\sqrt{6}$: $6 < 16$, so $\sqrt{6}<4$

Answer:

$\sqrt{24}$