https://file.aiquickdraw.com/mathbot/file/1726580503126829eimh6.jpg

The problem in the image asks you to estimate the value for:

\[
\sqrt{4.92 + 2.18 \times 7.31}
\]

To estimate, we round the numbers to make the calculation simpler:

- Round 4.92 to **5**.
- Round 2.18 to **2**.
- Round 7.31 to **7**.

Now substitute the rounded values into the expression:

\[
\sqrt{5 + 2 \times 7}
\]

First, calculate \(2 \times 7\):

\[
2 \times 7 = 14
\]

Now, add 5 to 14:

\[
5 + 14 = 19
\]

Finally, find the square root of 19. The square root of 19 is approximately 4.36.

Therefore, the estimated value for the expression is **about 4.36**.

Would you like further clarification or details on the steps?

Here are five related questions to expand this concept:

1. How would the estimate change if you round the numbers differently?
2. How can you calculate the exact value using a calculator instead of estimating?
3. What is the square root of 20, and how does it compare to 19?
4. How does rounding impact the accuracy of an estimate?
5. How would you estimate the cube root of a similar expression?

**Tip:** When estimating square roots, it's useful to memorize the square roots of small integers (e.g., \(\sqrt{16} = 4\), \(\sqrt{25} = 5\)) for quicker approximation.

Work out an estimate for √(4.92 + 2.18 × 7.31).

This solution explains how to estimate the square root of an expression with decimals by rounding the numbers and applying basic arithmetic. Suitable for students in Grades 7-9, the problem uses multiplication and square root properties.

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