If a = 3 and b = 4, what is the value of a² + b²?

To find the value of ( a^2 + b^2 ) when ( a = 3 ) and ( b = 4 ), you first need to square the values of ( a ) and ( b ).

Calculating ( a^2 ):

[

a^2 = 3^2 = 9

]

Calculating ( b^2 ):

[

b^2 = 4^2 = 16

]

Now, you add these two results together:

[

a^2 + b^2 = 9 + 16 = 25

]

Thus, the value of ( a^2 + b^2 ) is 25. This confirms that the answer is correct. Squaring the individual values and adding them is the fundamental approach to solving this type of problem. Other answer choices do not meet the requirements of this calculation, as they do not equal the total derived from the correct operations performed on ( a ) and ( b ).