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Simplify. Assume qq is greater than or equal to zero.\newline50q9\sqrt{50q^9}

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Full solution

Q. Simplify. Assume qq is greater than or equal to zero.\newline50q9\sqrt{50q^9}
  1. Factorize 50q950q^9: Factorize 50q950q^9 to find perfect squares.\newlineThe complete factorization of 50q950q^9 is 2×52×q8×q2 \times 5^2 \times q^8 \times q.
  2. Group perfect squares: Group the factors into perfect squares inside the radical. 50q9\sqrt{50q^9} becomes 2×52×q8×q\sqrt{2 \times 5^2 \times q^8 \times q}.
  3. Simplify expression: Simplify the expression by taking out the perfect squares from under the radical. 2×52×q8×q\sqrt{2 \times 5^2 \times q^8 \times q} simplifies to 5q4×2q5q^4 \times \sqrt{2q}.
  4. Write final expression: Write the final simplified expression.\newlineThe final simplified expression is 5q4×2q5q^4 \times \sqrt{2q}.

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