If $r = 19$, What Is $\sqrt{-3 + R}$?

Understanding the Problem

When dealing with mathematical expressions, it's essential to break down the problem step by step to arrive at the correct solution. In this case, we're given the value of $r$ as 19 and asked to find the value of $\sqrt{-3 + r}$. To solve this, we need to substitute the value of $r$ into the expression and then simplify it.

Substituting the Value of $r$

The first step is to substitute the value of $r$ into the expression $\sqrt{-3 + r}$. This means replacing $r$ with 19, resulting in $\sqrt{-3 + 19}$.

Simplifying the Expression

Now that we have the expression $\sqrt{-3 + 19}$, we can simplify it further. The expression inside the square root can be simplified by performing the subtraction: $-3 + 19 = 16$. Therefore, the expression becomes $\sqrt{16}$.

Evaluating the Square Root

The next step is to evaluate the square root of 16. The square root of a number is a value that, when multiplied by itself, gives the original number. In this case, the square root of 16 is 4, because $4 \times 4 = 16$.

Conclusion

In conclusion, when $r = 19$, the value of $\sqrt{-3 + r}$ is $\sqrt{16}$, which simplifies to 4.

Additional Considerations

It's worth noting that the expression $\sqrt{-3 + r}$ involves the square root of a negative number when $r$ is less than 3. However, in this case, $r$ is 19, which is greater than 3. Therefore, the expression simplifies to a positive value.

Real-World Applications

While the problem may seem abstract, it has real-world applications in various fields, such as physics and engineering. For example, in physics, the square root of a negative number can represent a complex number, which is used to describe oscillations and other phenomena.

Final Thoughts

In conclusion, the value of $\sqrt{-3 + r}$ when $r = 19$ is 4. This problem demonstrates the importance of following the order of operations and simplifying expressions step by step to arrive at the correct solution.

Common Mistakes to Avoid

When solving this problem, it's essential to avoid common mistakes such as:

• Not substituting the value of $r$ into the expression
• Not simplifying the expression inside the square root
• Not evaluating the square root correctly

Tips for Solving Similar Problems

To solve similar problems, follow these tips:

• Always substitute the given values into the expression
• Simplify the expression step by step
• Evaluate the square root correctly

Frequently Asked Questions

Q: What is the value of $\sqrt{-3 + r}$ when $r = 19$? A: The value of $\sqrt{-3 + r}$ when $r = 19$ is 4.

Q: Why is it essential to simplify the expression inside the square root? A: Simplifying the expression inside the square root helps to arrive at the correct solution.

Q: What are some real-world applications of the square root of a negative number? A: The square root of a negative number has real-world applications in physics and engineering, such as describing oscillations and other phenomena.

Conclusion

In conclusion, the value of $\sqrt{-3 + r}$ when $r = 19$ is 4. This problem demonstrates the importance of following the order of operations and simplifying expressions step by step to arrive at the correct solution.