Question

express in simplest radical form. \\(\sqrt{63}\\)

Explanation:

Step1: Factor the radicand

Factor 63 into its prime factors: \(63 = 9\times7\)

Step2: Apply the square root property

Use the property \(\sqrt{ab}=\sqrt{a}\times\sqrt{b}\) (where \(a\geq0\) and \(b\geq0\)): \(\sqrt{63}=\sqrt{9\times7}=\sqrt{9}\times\sqrt{7}\)

Step3: Simplify the square root of a perfect square

Since \(\sqrt{9} = 3\), we have: \(\sqrt{9}\times\sqrt{7}=3\sqrt{7}\)

Answer:

\(3\sqrt{7}\)