Question

simplify.
$6\sqrt{63}$

Explanation:

Step1: Factor 63 into prime factors

We know that \(63 = 9\times7\), and \(9 = 3^2\). So we can rewrite \(\sqrt{63}\) as \(\sqrt{9\times7}\).

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

\(\sqrt{9\times7}=\sqrt{9}\times\sqrt{7}\). Since \(\sqrt{9} = 3\), then \(\sqrt{9}\times\sqrt{7}=3\sqrt{7}\).

Step3: Multiply by the coefficient outside the square root

We have \(6\sqrt{63}=6\times3\sqrt{7}\).

Step4: Calculate \(6\times3\)

\(6\times3 = 18\), so \(6\sqrt{63}=18\sqrt{7}\).

Answer:

\(18\sqrt{7}\)