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 operation defined as \(a*b = a^2 + b^2\).

**Step 1: Calculate \(4 * 5\)**

Using the operation defined:
\[ 4 * 5 = 4^2 + 5^2 \]

Calculating \(4^2\) and \(5^2\):
\[ 4^2 = 16 \]
\[ 5^2 = 25 \]

Now, add these two results:
\[ 4 * 5 = 16 + 25 = 41 \]

**Step 2: Calculate \((4 * 5) * 3\)**

Now we need to evaluate \(41 * 3\) using the same operation:
\[ 41 * 3 = 41^2 + 3^2 \]

Calculating \(41^2\) and \(3^2\):
\[ 41^2 = 1681 \]
\[ 3^2 = 9 \]

Now, add these two results:
\[ 41 * 3 = 1681 + 9 = 1690 \]

Therefore, the value of \((4 * 5) * 3\) is \(1690\).

**Final Answer:**
\[ (4 * 5) * 3 = 1690 \]

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