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

Verified step by step guidance

1. Recognize that the expression involves multiplying two square roots: \( \sqrt{6} \times \sqrt{6} \).
2. Recall the property of square roots: \( \sqrt{a} \times \sqrt{a} = a \).
3. Apply this property to the expression: \( \sqrt{6} \times \sqrt{6} = 6 \).
4. Understand that this is because the square root and the square are inverse operations.
5. Conclude that the result of \( \sqrt{6} \times \sqrt{6} \) is simply the number under the square root, which is 6.

Key Concepts

Square Roots

A square root of a number 'x' is a value 'y' such that y² = x. For example, the square root of 6, denoted as √6, is a number that when multiplied by itself gives 6. Understanding square roots is essential for simplifying expressions involving radical signs.

Multiplication of Square Roots

When multiplying square roots, the product can be simplified using the property √a • √b = √(a • b). This means that the square roots can be combined under a single radical sign, which is crucial for simplifying expressions like √6 • √6.

Properties of Exponents

The operation of squaring a square root leads to the property that √x • √x = x. This property is fundamental in simplifying expressions involving square roots, as it allows for the direct conversion of the product of square roots back to the original number.