The table shows the diagonal lengths of TV screens at a store. 


**TV Screen Diagonal Lengths**

**Screen**

**Length**
**(feet)**

W

12.25−−−−√12.25

X

216216

Y

37144√37144

Z

8383


Which TV screen has the smallest diagonal length?

A.Screen W

B.Screen X

C.Screen Y

D.Screen Z


To determine which TV screen has the smallest diagonal length, we need to evaluate the lengths given for each screen.

Here are the diagonal lengths as provided in the table:

- **Screen W**: \( \sqrt{12.25} \)
- **Screen X**: 216
- **Screen Y**: \( \sqrt{37144} \)
- **Screen Z**: 83

Let's calculate each square root:

1. **Screen W**: \( \sqrt{12.25} = 3.5 \)
2. **Screen Y**: \( \sqrt{37144} \approx 192.75 \)

Now we compare all the lengths:

- **Screen W**: 3.5 feet
- **Screen X**: 216 feet
- **Screen Y**: 192.75 feet
- **Screen Z**: 83 feet

The smallest length among these is **3.5 feet**.

**Answer:** A. Screen W

Do you want more details or have any questions?

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Here are some related questions:

1. What is the square root of 144?
2. How do you approximate square roots for non-perfect squares?
3. What are some common diagonal lengths for TV screens in inches?
4. How do you convert feet to inches or centimeters?
5. What is the square root of 10000, and how does it compare to other values?
6. How can we use estimation to quickly compare large square roots?
7. What factors should be considered when choosing a TV screen size?
8. How would the area of a TV screen change if the diagonal length is doubled?

**Tip:** When dealing with square roots in practical situations, it's useful to have a sense of common square root values to quickly approximate and compare sizes.

Learn how to find the TV screen with the smallest diagonal length using square roots and comparison. This problem involves calculating square roots and comparing numerical values. Suitable for students in Grades 6-8.

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