Question

simplify.
$3\sqrt{27}$

Explanation:

Step1: Factor 27 into prime factors

We know that \(27 = 9\times3\), and \(9 = 3^2\), so \(27=3^2\times3\).

Step2: Simplify the square root

Using the property of square roots \(\sqrt{ab}=\sqrt{a}\times\sqrt{b}\) (where \(a = 3^2\) and \(b = 3\)), we have \(\sqrt{27}=\sqrt{3^2\times3}=\sqrt{3^2}\times\sqrt{3}=3\sqrt{3}\).

Step3: Multiply by the coefficient outside the square root

We have \(3\sqrt{27}=3\times3\sqrt{3}\).

Step4: Calculate the product of the coefficients

\(3\times3 = 9\), so \(3\sqrt{27}=9\sqrt{3}\).

Answer:

\(9\sqrt{3}\)