Approximate 31\sqrt{31} 
31
​
   to the nearest tenth.

We are tasked with approximating \( 31\sqrt{31} \) to the nearest tenth.

First, let’s calculate the value of \( \sqrt{31} \).

\[
\sqrt{31} \approx 5.57
\]

Now, multiplying by 31:

\[
31 \times 5.57 = 172.67
\]

To the nearest tenth, \( 31\sqrt{31} \approx 172.7 \).

Let me know if you have any questions or would like more details.

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Here are 5 related questions:
1. How do you approximate square roots of non-perfect squares?
2. What is the process to round numbers to the nearest tenth?
3. How would you approximate \( 32\sqrt{32} \) to the nearest tenth?
4. How does \( \sqrt{31} \) compare to \( \sqrt{32} \)?
5. Why does multiplying a number by its square root give an approximation close to that number's cube root?

**Tip:** When estimating square roots, consider memorizing the squares of integers for quicker approximations.

Approximate 31√31 to the nearest tenth.

Learn how to approximate the value of 31√31 to the nearest tenth with this step-by-step solution. This problem involves square root approximations, multiplication, and rounding, ideal for students in Grades 8-10.

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