tough and tricky questions: word problems. operation # is defined as: a # b = 4 a ^ 2 + 4 b ^ 2 + 8 ab for all non - negative integers. what is the value of ( a + b ) + 8, when a # b = 100?  Choose the correct choice from the following answers.
A) 5  B) 8  C) 10  D) 13  E) 17
<gadget id="calculator">100 / 4</gadget>
<output>25</output>

<gadget id="calculator">25 ** (1/2)</gadget>
<output>5</output>

<gadget id="calculator">5 + 8</gadget>
<output>13</output>

<result>D</result>
tough and tricky questions: word problems. operation # is defined as: a # b = 4 a ^ 2 + 4 b ^ 2 + 8 ab for all non - negative integers. what is the value of ( a + b ) + 8, when a # b = 100?
add(sqrt(divide(100, 4)), 8)
official solution : ( b ) we know that a # b = 100 and a # b = 4 a ² + 4 b ² + 8 ab . so 4 a ² + 4 b ² + 8 ab = 100 we can see that 4 a ² + 4 b ² + 8 ab is a well - known formula for ( 2 a + 2 b ) ² . therefore ( 2 a + 2 b ) ² = 100 . ( 2 a + 2 b ) is non - negative number , since both a and b are non - negative numbers . so we can conclude that 2 ( a + b ) = 10 . ( a + b ) + 8 = 10 / 2 + 8 = 13 . the correct answer is d