Question

Evaluate \(\sqrt{b^{2}-4 a c}\) for the given values. $$a=-3, b=7, c=5$$

Short answer

\(\sqrt{109}\)

Step-by-step solution

Substitute the values into the expression

Substitute the values \(a = -3\), \(b = 7\), and \(c = 5\) into the expression \(\sqrt{b^2 - 4ac}\) to get \(\sqrt{(7)^2 - 4(-3)(5)}\).

Simplify the expression inside the square root

First perform the multiplication and then the subtraction to get \(\sqrt{(7)^2 - 4(-3)(5)} = \sqrt{49 + 60} = \sqrt{109}\).

Simplify the square root

The number 109 is a prime number, so it cannot be simplified further. Therefore, the simplified form of \(\sqrt{b^2 - 4ac}\) with the given values is \(\sqrt{109}\).