Question

how can you estimate the side length of each square? a. estimate $\frac{sqrt{48}}{4}$. b. estimate $\frac{sqrt{96}}{4}$. c. estimate $sqrt{96}$. d. estimate $sqrt{48}$. the rectangle is units long and units wide. (round to the nearest tenth as needed.)

Explanation:

Step1: Find perfect - square approximations for 48

We know that $6^2 = 36$ and $7^2=49$. Since 48 is closer to 49, $\sqrt{48}\approx7.0$.

Step2: Find perfect - square approximations for 96

We know that $9^2 = 81$ and $10^2 = 100$. Since 96 is closer to 100, $\sqrt{96}\approx9.8$.

Step3: Calculate $\frac{\sqrt{96}}{4}$

$\frac{\sqrt{96}}{4}\approx\frac{9.8}{4}=2.45\approx2.5$.

Step4: Calculate $\frac{\sqrt{48}}{4}$

$\frac{\sqrt{48}}{4}\approx\frac{7.0}{4}=1.75\approx1.8$.

Answer:

For $\sqrt{48}\approx7.0$, for $\sqrt{96}\approx9.8$, for $\frac{\sqrt{96}}{4}\approx2.5$, for $\frac{\sqrt{48}}{4}\approx1.8$