Answer:
[tex]\sqrt{27}-6\sqrt3[/tex] = [tex]-3\sqrt3[/tex].
Step-by-step explanation:
Given:
The given expression to simplify is:
[tex]\sqrt{27}-6\sqrt3[/tex]
Now, 27 can be written as
[tex]27=3\times 3\times 3\\27=3^2\times 3[/tex]
Now, we know that for a square root function:
[tex]\sqrt{x^2}=x[/tex] and
[tex]\sqrt{xy}=\sqrt{x}\times \sqrt{y}[/tex]
Therefore, [tex]\sqrt{27}=\sqrt{3^2\times 3}=\sqrt{3^2}\times \sqrt{3}=3\sqrt{3}[/tex]
Now, plug in the value [tex]3\sqrt3[/tex] for [tex]\sqrt{27}[/tex]. This gives,
[tex]3\sqrt{3}-6\sqrt3[/tex]
[tex]\sqrt3[/tex] is a common factor in both the terms above. So, we factor it out. This gives,
[tex]\sqrt3(3-6)\\\sqrt3(-3)\\-3\sqrt3[/tex]
Therefore, the simplified answer is [tex]-3\sqrt3[/tex].
