Final Answer:
The simplified value of the expression √((-3)² + 4²) is 5.
Explanation:
The given expression is a square root of a quadratic equation, which can be written in the form of √(a² + b²). In this expression, the value of 'a' is -3 and the value of 'b' is 4. The simplified value of the expression can be obtained by applying the Pythagorean Theorem, which states that in a right triangle, the square of the hypotenuse (c) is equal to the sum of the squares of the other two sides (a and b). This theorem can be expressed mathematically as a² + b² = c².
In the given expression, the value of 'a' is -3 and the value of 'b' is 4. Substituting these values in the Pythagorean Theorem, we get: (-3)² + 4² = c². Solving the equation for 'c', we get: c² = (-3)² + 4². Taking the square root of both sides, we get: c = √((-3)² + 4²).
Therefore, the simplified value of the expression √((-3)² + 4²) is 5.