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Multiply. sqrt(2x)(sqrt5+2sqrt(3x)+sqrt8)

Multiply. 2x(5+23x+8) \sqrt{2 x}(\sqrt{5}+2 \sqrt{3 x}+\sqrt{8})

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Full solution

Q. Multiply. 2x(5+23x+8) \sqrt{2 x}(\sqrt{5}+2 \sqrt{3 x}+\sqrt{8})
  1. Distribute 2x\sqrt{2x}: Distribute 2x\sqrt{2x} across the terms inside the parentheses.\newlineCalculation: 2x(5+23x+8)=2x⋅5+2x⋅23x+2x⋅8\sqrt{2x}(\sqrt{5} + 2\sqrt{3x} + \sqrt{8}) = \sqrt{2x}\cdot\sqrt{5} + \sqrt{2x}\cdot2\sqrt{3x} + \sqrt{2x}\cdot\sqrt{8}
  2. Simplify terms: Simplify each term by multiplying the square roots.\newlineCalculation: 2x⋅5=10x\sqrt{2x}\cdot\sqrt{5} = \sqrt{10x}, 2x⋅23x=26x2\sqrt{2x}\cdot2\sqrt{3x} = 2\sqrt{6x^2}, 2x⋅8=16x\sqrt{2x}\cdot\sqrt{8} = \sqrt{16x}
  3. Further simplify square roots: Further simplify the square roots.\newlineCalculation: 10x\sqrt{10x}, 26x2=2⋅6⋅x2=2⋅6⋅x2\sqrt{6x^2} = 2\cdot\sqrt{6}\cdot\sqrt{x^2} = 2\cdot\sqrt{6}\cdot x, 16x=4x\sqrt{16x} = 4\sqrt{x}
  4. Combine all terms: Combine all terms.\newlineCalculation: 10x+26x+4x\sqrt{10x} + 2\sqrt{6}x + 4\sqrt{x}

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