Question

1. which of the following has the greatest value?

a. $pi + 1$
b. $sqrt{24}$
c. $\frac{9}{2}$
d. $4.overline{2}$

Explanation:

Step1: Approximate $\pi + 1$

We know that $\pi\approx3.14$, so $\pi + 1\approx3.14+1 = 4.14$.

Step2: Approximate $\sqrt{24}$

Since $4^2=16$ and $5^2 = 25$, and $24$ is close to $25$, $\sqrt{24}\approx4.9$.

Step3: Calculate $\frac{9}{2}$

$\frac{9}{2}=4.5$.

Step4: Analyze $4.\overline{2}$

$4.\overline{2}=4.222\cdots$.

Step5: Compare values

$4.14<4.222\cdots<4.5<4.9$, so $\sqrt{24}$ is the greatest.

Answer:

B. $\sqrt{24}$