CONCEPT PREVIEW Perform the operations mentally, and write the answers without doing intermediate steps. √6 • √6

Verified step by step guidance

1. Recall the property of square roots that states: \(\sqrt{a} \times \sqrt{a} = a\) for any positive number \(a\).
2. Apply this property to the given expression \(\sqrt{6} \times \sqrt{6}\).
3. Since both square roots are of the same number 6, multiply them directly using the property: \(\sqrt{6} \times \sqrt{6} = 6\).
4. Understand that this operation simplifies the expression by removing the square root, leaving just the number inside.
5. Therefore, the result of \(\sqrt{6} \times \sqrt{6}\) is simply 6.

Key Concepts

Square Roots and Radicals

A square root of a number is a value that, when multiplied by itself, gives the original number. The symbol √ denotes the square root. Understanding how to manipulate square roots is essential for simplifying expressions involving radicals.

Multiplication of Radicals

When multiplying two square roots, you can multiply the numbers inside the radicals directly: √a × √b = √(a × b). This property allows simplification of expressions without expanding intermediate steps.

Simplification of Radical Expressions

Simplifying radicals involves reducing the expression to its simplest form, often by recognizing perfect squares. For example, √6 × √6 equals √(6×6) = √36, which simplifies to 6, a whole number.