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

Verified step by step guidance

1. Identify the given radical expression. Here, it is \(\sqrt{2}\) divided by 3, which can be written as \(\frac{\sqrt{2}}{3}\).
2. Recall that squaring a fraction means squaring both the numerator and the denominator separately. So, \(\left(\frac{a}{b}\right)^2 = \frac{a^2}{b^2}\).
3. Apply the squaring operation to the numerator: \(\left(\sqrt{2}\right)^2\). Remember that squaring a square root cancels the root, so \(\left(\sqrt{2}\right)^2 = 2\).
4. Apply the squaring operation to the denominator: \$3^2 = 9$.
5. Combine the squared numerator and denominator to write the final expression as \(\frac{2}{9}\).

Key Concepts

Radical Expressions

A radical expression involves roots, such as square roots, indicated by the radical symbol (√). Understanding how to interpret and manipulate these expressions is essential, especially recognizing that √a represents the number which, when squared, equals a.

Squaring a Radical

Squaring a radical expression means raising it to the power of two. Since squaring and taking the square root are inverse operations, squaring √a results in a, provided a is non-negative. This simplifies expressions by eliminating the radical.

Properties of Exponents

When squaring expressions involving radicals, applying exponent rules is crucial. For example, (√a)^2 = a because √a = a^(1/2), and (a^(1/2))^2 = a^(1/2 * 2) = a. Understanding these properties helps in simplifying and solving radical expressions.