Problem

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

Solution

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 \(\boxed{12}\)

From Solvely APP
Source: https://solvelyapp.com/problems/Q9H3ZaXjMO/

Get free Solvely APP to solve your own problems!

solvely Solvely
Download