What is the square root of 17?

Steps to Solve

1. Identify the problem

We need to find the square root of 17, which can be written as $\sqrt{17}$.

2. Approximate the square root

Since 17 is not a perfect square, we look for perfect squares close to 17. $4^2 = 16$ and $5^2 = 25$. Since 17 is between 16 and 25, $\sqrt{17}$ will be between 4 and 5. As 17 is closer to 16 than it is to 25, we expect the square root to be closer to 4 than 5.

3. Refine approximation (optional)

To get a better approximation, we can try 4.1, 4.2, etc. $4.1^2 = 16.81$ and $4.2^2 = 17.64$. Since 17 is between 16.81 and 17.64, $\sqrt{17}$ is between 4.1 and 4.2. Since 17 is closer to 16.81, we expect the square root to be closer to 4.1 than 4.2.

4. Use a calculator

Using a calculator, we find that $\sqrt{17} \approx 4.1231056256...$.

answer

$\sqrt{17} \approx 4.123$

answer_info

The square root of 17 is an irrational number, meaning its decimal representation goes on forever without repeating. It is often rounded to a certain number of decimal places for practical use.

common_mistakes

A common mistake is assuming that the square root of a number will be a whole number. When the original number is not a perfect square, the square root will be an irrational number.

key_concepts

• Square roots
• Approximation
• Irrational numbers

concise_answer

$\sqrt{17} \approx 4.123$