Question

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c. estimate √74.
d. estimate √37.
the rectangle is □ units long and □ units wide.
(round to the nearest tenth as needed.)

Explanation:

Step1: Estimate $\sqrt{74}$

We know that $8^2 = 64$ and $9^2 = 81$. So $\sqrt{74}$ is between $8$ and $9$. Now, $74 - 64 = 10$ and $81 - 64 = 17$. So, $\sqrt{74}\approx 8 + \frac{10}{17}\approx 8.6$ (rounded to the nearest tenth).

Step2: Estimate $\sqrt{37}$

We know that $6^2 = 36$ and $7^2 = 49$. So $\sqrt{37}$ is between $6$ and $7$. Now, $37 - 36 = 1$ and $49 - 36 = 13$. So, $\sqrt{37}\approx 6 + \frac{1}{13}\approx 6.1$ (rounded to the nearest tenth).
Assuming the rectangle has length as $\sqrt{74}$ and width as $\sqrt{37}$ (or vice - versa), the length is approximately $8.6$ units and the width is approximately $6.1$ units (or length $6.1$ and width $8.6$).

Answer:

If length is $\sqrt{74}$ and width is $\sqrt{37}$: Length $\approx 8.6$ units, Width $\approx 6.1$ units.
If length is $\sqrt{37}$ and width is $\sqrt{74}$: Length $\approx 6.1$ units, Width $\approx 8.6$ units.