If `a*b=a^2+b^2,` then the value of `(4*5)*3` is

Options

A. `41^2 + 3^2`
B. `3^2 + 9^2`
C. `4^2+5^2 + 3^2`
D. None Of These

Explanation

To solve the problem, we need to evaluate the expression \((4*5)*3\) using the binary operation defined as \(a*b = a^2 + b^2\).

### Step-by-Step Solution:

1. **Calculate \(4*5\)**:
\[ 4*5 = 4^2 + 5^2 \]
- Calculate \(4^2\):
\[ 4^2 = 16 \]
- Calculate \(5^2\):
\[ 5^2 = 25 \]
- Now add them together:
\[ 4*5 = 16 + 25 = 41 \]

2. **Now calculate \((4*5)*3\)**, which is \(41*3\):
\[ 41*3 = 41^2 + 3^2 \]
- Calculate \(41^2\):
\[ 41^2 = 1681 \]
- Calculate \(3^2\):
\[ 3^2 = 9 \]
- Now add them together:
\[ 41*3 = 1681 + 9 = 1690 \]

### Final Result:
The value of \((4*5)*3\) is \(1690\).

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