Let's evaluate the given expression [tex]\( 2^2 + 3^2 = 4^2 \)[/tex] step-by-step to determine if it's a true statement.
1. Calculate [tex]\( 2^2 \)[/tex]:
[tex]\[
2^2 = 2 \times 2 = 4
\][/tex]
2. Calculate [tex]\( 3^2 \)[/tex]:
[tex]\[
3^2 = 3 \times 3 = 9
\][/tex]
3. Calculate [tex]\( 4^2\)[/tex]:
[tex]\[
4^2 = 4 \times 4 = 16
\][/tex]
4. Sum the results of [tex]\( 2^2 \)[/tex] and [tex]\( 3^2 \)[/tex]:
[tex]\[
2^2 + 3^2 = 4 + 9 = 13
\][/tex]
5. Compare the sum, [tex]\( 13 \)[/tex], to [tex]\( 4^2 \)[/tex], which is [tex]\( 16 \)[/tex]:
[tex]\[
13 \not= 16
\][/tex]
Since the left side of the equation, [tex]\( 13 \)[/tex], does not equal the right side, [tex]\( 16 \)[/tex], the statement [tex]\( 2^2 + 3^2 = 4^2 \)[/tex] is false.
Therefore, the correct answer is:
(B) No; [tex]\( 4 + 9 \neq 16 \)[/tex]
