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4sqrt(10 v)*sqrt(20v^(2))

410v⋅20v2 4 \sqrt{10 v} \cdot \sqrt{20 v^{2}}

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Full solution

Q. 410v⋅20v2 4 \sqrt{10 v} \cdot \sqrt{20 v^{2}}
  1. Find Product: Find the product of 410v4\sqrt{10v} and 20v2\sqrt{20v^{2}}.\newlineCalculation: 410v×20v2=410v×20v24\sqrt{10v} \times \sqrt{20v^{2}} = 4\sqrt{10v \times 20v^{2}}
  2. Simplify Inside: Simplify inside the square root.\newlineCalculation: 410v×20v2=4200v34\sqrt{10v \times 20v^{2}} = 4\sqrt{200v^{3}}
  3. Factor Perfect Squares: Factor out perfect squares from the square root.\newlineCalculation: 4200v3=4100v2⋅2v4\sqrt{200v^{3}} = 4\sqrt{100v^{2} \cdot 2v}
  4. Take Square Root: Take the square root of the perfect squares.\newlineCalculation: 4100v2⋅2v=4⋅10v⋅2v4\sqrt{100v^{2} \cdot 2v} = 4 \cdot 10v \cdot \sqrt{2v}
  5. Multiply Numbers: Multiply the numbers outside the square root.\newlineCalculation: 4×10v×2v=40v×2v4 \times 10v \times \sqrt{2v} = 40v \times \sqrt{2v}
  6. Check Simplification: Check for any further simplification.\newlineNo further simplification is possible.

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