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Simplify. Remove all perfect squares from inside the square root. Assume a is positive. sqrt(108a^(6))=◻

Simplify.\newlineRemove all perfect squares from inside the square root. Assume \newlineaa is positive.\newline108a6\sqrt{108a^{6}}=□\square

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Full solution

Q. Simplify.\newlineRemove all perfect squares from inside the square root. Assume \newlineaa is positive.\newline108a6\sqrt{108a^{6}}=□\square
  1. Pair perfect squares: Next, we can pair the perfect squares under the square root: 22×33×a6=22×32×3×a2×a2×a2.\sqrt{2^2 \times 3^3 \times a^6} = \sqrt{2^2 \times 3^2 \times 3 \times a^2 \times a^2 \times a^2}.
  2. Take out perfect squares: Now, we can take out the perfect squares from under the square root: 22×32×3×a2×a2×a2=2×3×a×a×a×3\sqrt{2^2 \times 3^2 \times 3 \times a^2 \times a^2 \times a^2} = 2 \times 3 \times a \times a \times a \times \sqrt{3}. This simplifies to: 6a3×36a^3 \times \sqrt{3}.

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