Question

simplify.
\sqrt{63}

Explanation:

Step1: Factor 63 into prime factors

We know that \( 63 = 9\times7 \), and \( 9 = 3^2 \), so \( 63=3^2\times7 \).

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

\(\sqrt{63}=\sqrt{3^2\times7}=\sqrt{3^2}\times\sqrt{7}\)

Step3: Simplify \(\sqrt{3^2}\)

Since \(\sqrt{3^2} = 3\) (because the square root of a square of a non - negative number is the number itself), we have \(\sqrt{63}=3\sqrt{7}\)

Answer:

\(3\sqrt{7}\)