Question

(6 + √27) / 3 Sorry i wrote it wrong the first time.

Answer 1

Answer:
`2 + √(3)`

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Work Shown:

`(6 + √(27))/(3)\\\\(6 + √(9*3))/(3)\\\\(6 + √(9)*√(3))/(3)\\\\(6 + 3√(3))/(3)\\\\(3(2 + √(3)))/(3)\\\\2 + √(3)\\\\`

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.

Answer 2

3.73205081 i think it right hope it helps