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Simplify. Assume aa is greater than or equal to zero.\newline18a4\sqrt{18a^4}

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Full solution

Q. Simplify. Assume aa is greater than or equal to zero.\newline18a4\sqrt{18a^4}
  1. Factorize 18a418a^4: Factorize 18a418a^4 to find perfect squares.\newlineThe complete factorization of 18a418a^4 is 2×3×3×a2×a22 \times 3 \times 3 \times a^2 \times a^2.
  2. Group perfect squares: Group the factors into perfect squares inside the radical. 18a4\sqrt{18a^4} becomes 2×32×a2×a2\sqrt{2 \times 3^2 \times a^2 \times a^2}.
  3. Simplify square root: Simplify the square root of the perfect squares. 2×32×a2×a2\sqrt{2 \times 3^2 \times a^2 \times a^2} simplifies to 3×a2×23 \times a^2 \times \sqrt{2}.
  4. Write final expression: Write the final simplified expression.\newlineThe final simplified expression is 3a2⋅23a^2 \cdot \sqrt{2}.

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