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Simplify. Assume ff is greater than or equal to zero.\newline75f9\sqrt{75f^9}

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Full solution

Q. Simplify. Assume ff is greater than or equal to zero.\newline75f9\sqrt{75f^9}
  1. Factor Perfect Squares: Factor the expression under the square root to identify perfect squares.\newlineWhat is the complete factorization of 75f975f^9?\newlineComplete factorization of 75f9=3×52×f8×f75f^9 = 3 \times 5^2 \times f^8 \times f
  2. Group Factors: Group the factors into perfect squares and separate the non-perfect square. 75f9\sqrt{75f^9} will become 3×52×f8×f\sqrt{3 \times 5^2 \times f^8 \times f} What is the expression after making perfect squares inside the radical? 75f9=3×(52)×(f8)×f\sqrt{75f^9} = \sqrt{3 \times (5^2) \times (f^8) \times f}
  3. Simplify Radical: Simplify the square root of the perfect squares and leave the non-perfect square inside the radical. 3×(52)×(f8)×f=5×f4×3f\sqrt{3 \times (5^2) \times (f^8) \times f} = 5 \times f^4 \times \sqrt{3f}
  4. Final Expression: Write the final simplified expression.\newlineThe simplified expression is 5f4×3f5f^4 \times \sqrt{3f}.

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