Question

question
express in simplest radical form.
\sqrt{63}

Explanation:

Step1: Factor 63 into prime factors

We know that \(63 = 9\times7\), where 9 is a perfect square. So we can rewrite \(\sqrt{63}\) as \(\sqrt{9\times7}\).

Step2: Use the property of square roots \(\sqrt{ab}=\sqrt{a}\times\sqrt{b}\) (for \(a\geq0,b\geq0\))

Applying this property, we get \(\sqrt{9\times7}=\sqrt{9}\times\sqrt{7}\).

Step3: Simplify \(\sqrt{9}\)

Since \(3^2 = 9\), \(\sqrt{9}=3\). So the expression becomes \(3\sqrt{7}\).

Answer:

\(3\sqrt{7}\)