Find the square of each radical expression. See Example 2.√2 3

Verified step by step guidance

1. Identify the expression to be squared: \( \sqrt{2} \).
2. Recall that squaring a square root cancels the square root: \( (\sqrt{a})^2 = a \).
3. Apply this property to the expression: \( (\sqrt{2})^2 = 2 \).
4. Identify the second expression to be squared: \( 3 \).
5. Square the number: \( 3^2 = 9 \).

Key Concepts

Radical Expressions

Radical expressions involve roots, such as square roots, cube roots, etc. The square root of a number 'x' is a value that, when multiplied by itself, gives 'x'. Understanding how to manipulate these expressions is crucial for simplifying and solving equations that involve roots.

Squaring a Radical

Squaring a radical expression means multiplying the radical by itself. For example, squaring √2 results in (√2)² = 2. This process eliminates the radical and provides a straightforward numerical result, which is essential for solving problems involving radicals.

Properties of Exponents

The properties of exponents govern how to handle powers and roots in mathematical expressions. For instance, the property (a^m)² = a^(2m) helps in simplifying expressions involving radicals. Familiarity with these properties is vital for effectively manipulating and solving equations that include radical terms.