What Is The Square Root Of $r^{64}$?A. $r^4$ B. $ R 8 R^8 R 8 [/tex] C. $r^{16}$ D. $r^{32}$
Understanding the Concept of Square Root
The square root of a number is a value that, when multiplied by itself, gives the original number. In mathematical terms, if we have a number 'x', then its square root is denoted by √x and is a value that satisfies the equation x = (√x)^2. This concept is crucial in mathematics, particularly in algebra and geometry.
Applying the Concept to $r^{64}$
To find the square root of $r^{64}$, we need to understand the properties of exponents. When we have a number raised to a power, we can find its square root by taking the square root of the base and dividing the exponent by 2. In this case, we have $r^{64}$, and we want to find its square root.
Using the Properties of Exponents
Using the properties of exponents, we can rewrite $r^{64}$ as (r32)2. This is because when we have a number raised to a power, we can rewrite it as the base raised to the power of the exponent multiplied by the power. In this case, we have (r32)2, which is equivalent to $r^{64}$.
Finding the Square Root
Now that we have rewritten $r^{64}$ as (r32)2, we can find its square root by taking the square root of the base and dividing the exponent by 2. The square root of r^32 is r^16, and when we divide the exponent by 2, we get 16/2 = 8. However, we are looking for the square root of the entire expression, not just the base. Therefore, we need to take the square root of the entire expression, which is (r16)2.
Simplifying the Expression
When we simplify the expression (r16)2, we get r^32. However, this is not the correct answer. We need to find the square root of the entire expression, not just the base. Therefore, we need to take the square root of the entire expression, which is √(r^32).
Final Answer
The final answer is √(r^32), which is equivalent to r^16. However, this is not among the answer choices. We need to find the correct answer among the options provided.
Analyzing the Answer Choices
Let's analyze the answer choices:
A. $r^4$ B. $r^8$ C. $r^{16}$ D. $r^{32}$
We know that the square root of $r^{64}$ is $r^{32}$, but this is not among the answer choices. However, we can see that $r^{16}$ is the square root of $r^{32}$, which is the correct answer.
Conclusion
In conclusion, the square root of $r^{64}$ is $r^{32}$, but this is not among the answer choices. However, we can see that $r^{16}$ is the square root of $r^{32}$, which is the correct answer. Therefore, the correct answer is C. $r^{16}$.
Frequently Asked Questions
- What is the square root of $r^{64}$? The square root of $r^{64}$ is $r^{32}$.
- How do we find the square root of a number raised to a power? We can find the square root of a number raised to a power by taking the square root of the base and dividing the exponent by 2.
- What is the correct answer among the options provided? The correct answer is C. $r^{16}$.
Final Answer
The final answer is C. $r^{16}$.
Q: What is the square root of $r^{64}$?
A: The square root of $r^{64}$ is $r^{32}$.
Q: How do we find the square root of a number raised to a power?
A: We can find the square root of a number raised to a power by taking the square root of the base and dividing the exponent by 2.
Q: What is the correct answer among the options provided?
A: The correct answer is C. $r^{16}$.
Q: Why is $r^{16}$ the correct answer?
A: $r^{16}$ is the correct answer because it is the square root of $r^{32}$, which is the square root of $r^{64}$.
Q: Can you explain the concept of square root in more detail?
A: The square root of a number is a value that, when multiplied by itself, gives the original number. In mathematical terms, if we have a number 'x', then its square root is denoted by √x and is a value that satisfies the equation x = (√x)^2.
Q: How do we apply the concept of square root to $r^{64}$?
A: To find the square root of $r^{64}$, we need to understand the properties of exponents. When we have a number raised to a power, we can find its square root by taking the square root of the base and dividing the exponent by 2.
Q: What are the properties of exponents?
A: The properties of exponents state that when we have a number raised to a power, we can rewrite it as the base raised to the power of the exponent multiplied by the power. In this case, we have (r32)2, which is equivalent to $r^{64}$.
Q: How do we simplify the expression (r16)2?
A: When we simplify the expression (r16)2, we get r^32. However, this is not the correct answer. We need to find the square root of the entire expression, not just the base.
Q: What is the final answer?
A: The final answer is C. $r^{16}$.
Q: Why is C. $r^{16}$ the correct answer?
A: C. $r^{16}$ is the correct answer because it is the square root of $r^{32}$, which is the square root of $r^{64}$.
Q: Can you provide more examples of finding the square root of a number raised to a power?
A: Yes, here are a few examples:
- The square root of $r^{25}$ is $r^{12.5}$
- The square root of $r^{36}$ is $r^{18}$
- The square root of $r^{49}$ is $r^{24.5}$
Q: How do we apply the concept of square root to these examples?
A: To find the square root of a number raised to a power, we need to understand the properties of exponents. When we have a number raised to a power, we can find its square root by taking the square root of the base and dividing the exponent by 2.
Q: What are the properties of exponents in these examples?
A: The properties of exponents state that when we have a number raised to a power, we can rewrite it as the base raised to the power of the exponent multiplied by the power. In these examples, we have:
- (r12.5)2 = r^25
- (r18)2 = r^36
- (r24.5)2 = r^49
Q: How do we simplify these expressions?
A: When we simplify these expressions, we get:
- r^25
- r^36
- r^49
Q: What is the final answer for these examples?
A: The final answer for these examples is:
- The square root of $r^{25}$ is $r^{12.5}$
- The square root of $r^{36}$ is $r^{18}$
- The square root of $r^{49}$ is $r^{24.5}$