Determine the value of the given mathematical expression:
$\sqrt{13^{2}-5^{2}}$

Answer

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Answer

Final Answer: The value of the given mathematical expression is $\boxed{12}$

Steps

Step 1 ：Given the mathematical expression $\sqrt{13^{2}-5^{2}}$

Step 2 ：Recognize this as a difference of squares, which can be simplified using the formula $\sqrt{a^{2}-b^{2}} = \sqrt{(a+b)(a-b)}$

Step 3 ：Let $a=13$ and $b=5$

Step 4 ：Simplify the expression inside the square root as $\sqrt{(13+5)(13-5)}$

Step 5 ：Calculate the expression inside the square root to get 144

Step 6 ：Take the square root of 144 to get the final answer

Step 7 ：Final Answer: The value of the given mathematical expression is $\boxed{12}$