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sqrt(4x^(5))-xsqrt(x^(3))

8080. 4x5−xx3 \sqrt{4 x^{5}}-x \sqrt{x^{3}}

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Full solution

Q. 8080. 4x5−xx3 \sqrt{4 x^{5}}-x \sqrt{x^{3}}
  1. Identify square root: Identify the square root of 4x54x^5.4x5=4⋅x5=2x52\sqrt{4x^5} = \sqrt{4}\cdot\sqrt{x^5} = 2x^{\frac{5}{2}}
  2. Combine expressions: Identify the square root of x3x^3.x3=x32\sqrt{x^3} = x^{\frac{3}{2}}
  3. Subtract like terms: Combine the two expressions.\newline2x5/2−x⋅x3/2=2x5/2−x1+3/2=2x5/2−x5/22x^{5/2} - x\cdot x^{3/2} = 2x^{5/2} - x^{1+3/2} = 2x^{5/2} - x^{5/2}
  4. Subtract like terms: Combine the two expressions.\newline2x52−x⋅x32=2x52−x1+32=2x52−x522x^{\frac{5}{2}} - x \cdot x^{\frac{3}{2}} = 2x^{\frac{5}{2}} - x^{1+\frac{3}{2}} = 2x^{\frac{5}{2}} - x^{\frac{5}{2}} Subtract the like terms.\newline2x52−x52=x522x^{\frac{5}{2}} - x^{\frac{5}{2}} = x^{\frac{5}{2}}

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