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Simplify. Assume qq is greater than or equal to zero.\newline12q10\sqrt{12q^{10}}

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Full solution

Q. Simplify. Assume qq is greater than or equal to zero.\newline12q10\sqrt{12q^{10}}
  1. Factorize Perfect Squares: Factorize the expression under the square root to identify perfect squares.\newlineThe complete factorization of 12q1012q^{10} is 2×2×3×q102 \times 2 \times 3 \times q^{10}. We can rewrite q10q^{10} as (q5)2(q^{5})^{2} to identify the perfect square.
  2. Separate Perfect Squares: Rewrite the square root of the expression by separating the perfect squares from the non-perfect squares. 12q10\sqrt{12q^{10}} becomes 2×2×3×(q5)2\sqrt{2 \times 2 \times 3 \times (q^5)^2}.
  3. Simplify Square Root: Simplify the square root by taking out the perfect squares. 2×2×3×(q5)2\sqrt{2 \times 2 \times 3 \times (q^5)^2} simplifies to 2×q5×32 \times q^5 \times \sqrt{3}, because 22=2\sqrt{2^2} = 2 and (q5)2=q5\sqrt{(q^5)^2} = q^5.

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