The problem in the image asks to calculate $\sqrt{8.52^2 - 4.13^2}$ and provide the answer to:

1. 3 significant figures.
2. 3 decimal places.

Let's solve the expression step by step:

Expression:

$\sqrt{8.52^2 - 4.13^2}$

1. First, calculate $8.52^2$: $8.52^2 = 72.5904$

2. Next, calculate $4.13^2$: $4.13^2 = 17.0569$

3. Now, subtract the squares: $72.5904 - 17.0569 = 55.5335$

4. Finally, take the square root: $\sqrt{55.5335} \approx 7.451$

Now let's round this result:

• (a) To 3 significant figures: The answer is 7.45.
• (b) To 3 decimal places: The answer is 7.451.

Would you like further details or have any questions?

Here are 5 related questions to expand on this topic:

1. What is the difference between significant figures and decimal places?
2. How does rounding affect the accuracy of a calculation?
3. How do you handle square roots when simplifying algebraic expressions?
4. Can you always apply the Pythagorean Theorem to solve expressions like this?
5. How would this problem change if the values inside the square root were negative?

Tip: When rounding, always be mindful of whether you're rounding up or down depending on the digit immediately after the cutoff point!