If an operation is defined by a* b = a² + b², then (1 * 2) * 6 is

The correct answer is 61.

Step-by-Step Explanation:

We are given a custom binary operation denoted by * which is defined as:
a * b = a 2 + b 2 This definition tells us that performing the operation on any two numbers is equivalent to squaring the first number, squaring the second number, and then adding the two squares together.

We need to evaluate the expression:
( 1 * 2 ) * 6 According to the standard order of operations, we must first evaluate the expression inside the parentheses: 1*2.

Step 1: Evaluate the parentheses (1*2)
Using the operation rule with a=1 and b=2:
1 * 2 = 1 2 + 2 2 Calculating the squares:
1 2 = 1
2 2 = 4 Adding the values together:
1 * 2 = 1 + 4 = 5

Step 2: Substitute the result back into the main expression
Now, we replace (1*2) with 5 in our original expression:
( 1 * 2 ) * 6 = 5 * 6 We now apply the custom operation rule to 5*6, with a=5 and b=6:
5 * 6 = 5 2 + 6 2 Calculating the squares:
5 2 = 25
6 2 = 36 Adding the values together:
5 * 6 = 25 + 36 = 61

Therefore, the value of (1*2)*6 is 61.