Question
Jenny says that √2⁶ will be 6. Is she right? Give reasons for your answer.
Answers
GPT-4o mini
No, Jenny is not correct.
To understand why, let's break down the expression \( \sqrt{2^6} \).
1. First, we can rewrite the square root in terms of exponents:
\[
\sqrt{2^6} = (2^6)^{1/2}
\]
2. When we raise a power to a power, we multiply the exponents:
\[
(2^6)^{1/2} = 2^{6 \cdot \frac{1}{2}} = 2^3
\]
3. Now, we can evaluate \( 2^3 \):
\[
2^3 = 2 \times 2 \times 2 = 8
\]
Thus, \( \sqrt{2^6} = 8 \), not 6. Therefore, Jenny's assertion that \( \sqrt{2^6} \) is 6 is incorrect. The correct answer is 8.
To understand why, let's break down the expression \( \sqrt{2^6} \).
1. First, we can rewrite the square root in terms of exponents:
\[
\sqrt{2^6} = (2^6)^{1/2}
\]
2. When we raise a power to a power, we multiply the exponents:
\[
(2^6)^{1/2} = 2^{6 \cdot \frac{1}{2}} = 2^3
\]
3. Now, we can evaluate \( 2^3 \):
\[
2^3 = 2 \times 2 \times 2 = 8
\]
Thus, \( \sqrt{2^6} = 8 \), not 6. Therefore, Jenny's assertion that \( \sqrt{2^6} \) is 6 is incorrect. The correct answer is 8.