In Exercises 29–36, simplify and write the result in standard form. ____________√1² − 4 ⋅ 0.5 ⋅ 5

Verified step by step guidance

1. Identify the expression under the square root: \(1^2 - 4 \cdot 0.5 \cdot 5\).
2. Calculate \(1^2\), which is simply 1.
3. Compute the product \(4 \cdot 0.5 \cdot 5\).
4. Subtract the result of the product from 1.
5. Take the square root of the resulting value to simplify the expression.

Key Concepts

Square Root

The square root of a number is a value that, when multiplied by itself, gives the original number. In this context, understanding how to simplify expressions under the square root is crucial. For example, √(a²) simplifies to 'a', and knowing how to handle constants and variables under the square root is essential for solving the problem.

Standard Form

Standard form in mathematics typically refers to expressing numbers in a conventional way, such as a + bi for complex numbers or a simplified radical form for square roots. In this exercise, it involves simplifying the expression under the square root and ensuring the final result is presented clearly, which may include rationalizing the denominator if necessary.

Quadratic Expression

The expression inside the square root, 1² - 4 ⋅ 0.5 ⋅ 5, is a quadratic expression. Recognizing the structure of quadratic expressions helps in simplifying them effectively. The expression can be evaluated using the quadratic formula or by direct calculation, which is essential for determining the value under the square root before simplification.