What is the square root of 32 rounded to the nearest tenth?
The Correct Answer and Explanation is:
The square root of 32 rounded to the nearest tenth is 5.7.
Explanation:
To understand why the square root of 32 is approximately 5.7, let’s explore both the mathematical process and the concept behind square roots.
A square root of a number is a value that, when multiplied by itself, gives the original number. In this case, we are looking for a number that, when squared, gives 32.
We know some perfect squares close to 32:
- √25 = 5 (since 5 × 5 = 25)
- √36 = 6 (since 6 × 6 = 36)
So, √32 is between 5 and 6. To find a more precise value, we can try squaring numbers between 5 and 6:
- 5.5² = 30.25 → too low
- 5.6² = 31.36 → still too low
- 5.7² = 32.49 → slightly too high
- 5.65² = 31.9225 → close
- 5.66² = 32.0356 → very close
From these calculations, we see that √32 is slightly less than 5.7, but because we are rounding to the nearest tenth, we look at the digit in the hundredths place.
The actual square root of 32 is:32≈5.656854249\sqrt{32} ≈ 5.65685424932≈5.656854249
The digit in the tenths place is 5, and the digit in the hundredths place is 6, which means we round up.
So:
- Tenths place: 5
- Hundredths place: 6 → round the tenths place up from 5 to 6
But since 5.656… rounds to 5.7 (not 5.6), our final answer is:5.7\boxed{5.7}5.7
This result is useful in estimation and in problems involving measurement, geometry, and algebra where irrational numbers must be simplified for practical use
