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sqrt150

150 \sqrt{150}

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Full solution

Q. 150 \sqrt{150}
  1. Identify Prime Factors: Identify the prime factors of 150150.150=2×3×5×5150 = 2 \times 3 \times 5 \times 5
  2. Group Identical Factors: Group the identical factors and use exponents. 150=2×3×52\sqrt{150} = \sqrt{2 \times 3 \times 5^2}
  3. Apply Product Property: Apply the product property of radicals. 150=2×3×52\sqrt{150} = \sqrt{2} \times \sqrt{3} \times \sqrt{5^2}
  4. Simplify Perfect Square: Simplify the square root of the perfect square. 150=2×3×5\sqrt{150} = \sqrt{2} \times \sqrt{3} \times 5
  5. Combine Non-Perfect Square Roots: Combine the non-perfect square roots and multiply by the outside number. 150=5×2×3\sqrt{150} = 5 \times \sqrt{2 \times 3}
  6. Finish Simplifying: Finish simplifying by multiplying the square roots. 150=5×6\sqrt{150} = 5 \times \sqrt{6}

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