what is the square root of 14 to the nearest tenth

what is the square root of 14 to the nearest tenth

The Correct Answer and Explanation is:

The square root of 14 is approximately 3.7 when rounded to the nearest tenth.

Here’s a step-by-step explanation:

1. Understanding Square Roots: The square root of a number is a value that, when multiplied by itself, gives the original number. In mathematical notation, the square root of a number nnn is written as n\sqrt{n}n​.
2. Calculating the Square Root of 14: To find the square root of 14, we can either use a calculator or estimate it. For numbers that aren’t perfect squares (like 14), the square root will be a non-repeating, non-terminating decimal. The square roots of numbers around 14 are:
   • 9=3\sqrt{9} = 39​=3
   • 16=4\sqrt{16} = 416​=4
   Since 14 is between 9 and 16, we know that 14\sqrt{14}14​ will be between 3 and 4.
3. Approximating with a Calculator: Using a calculator, we get: 14≈3.741657…\sqrt{14} \approx 3.741657 \ldots14​≈3.741657…
4. Rounding to the Nearest Tenth: The first digit after the decimal is 7, which means we round up. Therefore, 14\sqrt{14}14​ to the nearest tenth is 3.7.
5. Conclusion: The square root of 14 rounded to the nearest tenth is 3.7. This approximation is quite accurate for most practical purposes, although the exact value of the square root is an irrational number with infinite decimal places.

This process helps illustrate how square roots work and how we can estimate and round them for simplicity.