Use the rules for radicals to perform the indicated operations. Assume all variable expressions represent positive real numbers. √11 • √44

Verified step by step guidance

1. insert step 1> Start by using the property of radicals that states $\sqrt{a}\cdot \sqrt{b}=\sqrt{a\cdot b}$. Apply this to the expression $\sqrt{11}\cdot \sqrt{44}$.
2. insert step 2> Multiply the numbers under the radicals: $11\cdot 44$.
3. insert step 3> Calculate the product of 11 and 44 to get a single number under the square root.
4. insert step 4> Simplify the resulting square root by finding any perfect square factors.
5. insert step 5> Express the simplified form of the square root, if possible, by taking out any perfect squares.

Key Concepts

Properties of Radicals

The properties of radicals include rules that govern the manipulation of square roots and other roots. Key properties include the product rule, which states that the square root of a product is the product of the square roots, and the quotient rule, which allows for the simplification of square roots of fractions. Understanding these properties is essential for performing operations involving radicals.

Simplifying Radicals

Simplifying radicals involves expressing a radical in its simplest form, which often includes factoring out perfect squares. For example, √44 can be simplified to √(4*11) = 2√11. This process is crucial for making calculations easier and clearer, especially when performing operations like multiplication or addition with radicals.

Assumptions about Variables

In this context, the assumption that all variable expressions represent positive real numbers is important because it ensures that the square roots are defined and yield real numbers. This assumption eliminates complications that arise from negative values, which would lead to imaginary numbers. It is a fundamental aspect of working with radicals in algebra.