Use the quotient rule to simplify the expressions in Exercises 45-46. √(121/4)

Verified step by step guidance

1. Identify the expression under the square root: \( \frac{121}{4} \).
2. Recognize that the square root of a quotient can be expressed as the quotient of the square roots: \( \sqrt{\frac{121}{4}} = \frac{\sqrt{121}}{\sqrt{4}} \).
3. Calculate the square root of the numerator: \( \sqrt{121} = 11 \).
4. Calculate the square root of the denominator: \( \sqrt{4} = 2 \).
5. Express the simplified form of the original expression as a fraction: \( \frac{11}{2} \).

Key Concepts

Quotient Rule

The quotient rule is a fundamental principle in calculus used to differentiate functions that are expressed as the ratio of two other functions. It states that if you have a function f(x) = g(x)/h(x), the derivative f'(x) can be found using the formula f'(x) = (g'(x)h(x) - g(x)h'(x)) / (h(x))^2. Understanding this rule is essential for simplifying and differentiating expressions involving division.

Simplifying Radicals

Simplifying radicals involves reducing a square root expression to its simplest form. For example, √(a/b) can be simplified to √a/√b, provided that both a and b are non-negative. This concept is crucial when dealing with expressions like √(121/4), as it allows for easier manipulation and understanding of the underlying values.

Properties of Square Roots

The properties of square roots include rules that govern how to handle square roots in mathematical expressions. Key properties include √(a*b) = √a * √b and √(a/b) = √a / √b. These properties are vital for simplifying expressions involving square roots, such as the one presented in the question, and help in breaking down complex expressions into more manageable parts.