simplify.\n$3\\sqrt{27}$

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\geq0,b\geq0)), we have (\sqrt{27}=\sqrt{3^2\times3}=\sqrt{3^2}\times\sqrt{3}). Since (\sqrt{3^2} = 3) (because the square root of a square of a non - negative number is the number itself), then (\sqrt{27}=3\sqrt{3}).

Step3: Multiply by the coefficient outside the square root

We have (3\sqrt{27}=3\times(3\sqrt{3})). Using the associative property of multiplication, (3\times3\sqrt{3}=9\sqrt{3}).

Answer:

(9\sqrt{3})