Question

simplify: \\(sqrt{324}\\)

1. write the prime factorization of the radicand.

\\(sqrt{324} = sqrt{2cdot2cdot3cdot3cdot3cdot3}\\)

1. apply the product property of square roots. write the radicand as a product, forming as many perfect square roots as possible.

\\(sqrt{2cdot2cdot3cdot3cdot3cdot3} = sqrt{2^2} cdot sqrt{3^2} cdot sqrt{3^2}\\)

1. simplify.

\\(sqrt{324} = square\\)

Explanation:

Step1: Recall square root of square

For any non - negative real number \(a\), \(\sqrt{a^{2}}=a\). So we simplify each square root term: \(\sqrt{2^{2}} = 2\), \(\sqrt{3^{2}}=3\), \(\sqrt{3^{2}} = 3\).

Step2: Multiply the simplified terms

Now we multiply the results: \(2\times3\times3\).
First, \(2\times3 = 6\), then \(6\times3=18\).

Answer:

\(18\)