Respuesta :
Answer: [tex]2 + \sqrt{3}[/tex]
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Work Shown:
[tex]\frac{6 + \sqrt{27}}{3}\\\\\frac{6 + \sqrt{9*3}}{3}\\\\\frac{6 + \sqrt{9}*\sqrt{3}}{3}\\\\\frac{6 + 3\sqrt{3}}{3}\\\\\frac{3(2 + \sqrt{3})}{3}\\\\2 + \sqrt{3}\\\\[/tex]
The idea with simplifying the square root (steps 2 through 4) has us factoring 27 so that one factor is a perfect square. We want the largest perfect square factor possible.
That way when we use the rule sqrt(x*y) = sqrt(x)*sqrt(y), we pull out that perfect square to then use the rule sqrt(x^2) = x where x is nonnegative.
After simplifying the square root, we factor out the GCF and then cancel out the 3's.
