To solve the equation [tex]\((\sqrt{2})^2 = 2^8\)[/tex], let's break this down step by step.
1. Understand the left side of the equation:
- The left side is [tex]\((\sqrt{2})^2\)[/tex].
- When you square a square root, you get the number under the square root.
- So, [tex]\((\sqrt{2})^2 = 2\)[/tex].
2. Understand the right side of the equation:
- The right side is [tex]\(2^8\)[/tex].
- [tex]\(2^8\)[/tex] means raising 2 to the power of 8.
- This multiplication would be expressed as [tex]\(2 \times 2 \times 2 \times 2 \times 2 \times 2 \times 2 \times 2 = 256\)[/tex].
3. Compare both sides:
- The left side is 2.
- The right side is 256.
So, [tex]\((\sqrt{2})^2 = 2\)[/tex] and [tex]\(2^8 = 256\)[/tex].
Therefore, the two sides of the initial equation are not equal:
[tex]\[ 2 \neq 256. \][/tex]
