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Simplify.

6sqrt27

Simplify.\newline627 6 \sqrt{27}

Full solution

Q. Simplify.\newline627 6 \sqrt{27}
  1. Break down into prime factors: First, let's break down 2727 into its prime factors.\newline27=3×3×327 = 3 \times 3 \times 3
  2. Rewrite using prime factors: Now, we rewrite the square root of 2727 using its prime factors.627=6×3×3×36\sqrt{27} = 6 \times \sqrt{3 \times 3 \times 3}
  3. Group identical factors: Next, we group the identical factors under the square root.\newline6×3×3×3=6×32×36 \times \sqrt{3 \times 3 \times 3} = 6 \times \sqrt{3^2 \times 3}
  4. Take out of square root: We know that 32\sqrt{3^2} is just 33, so we can take it out of the square root.6×32×3=6×3×36 \times \sqrt{3^2 \times 3} = 6 \times 3 \times \sqrt{3}
  5. Multiply outside numbers: Now, we multiply the numbers outside the square root. 6×3×3=1836 \times 3 \times \sqrt{3} = 18\sqrt{3}

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