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(2sqrt18+sqrtx)/(sqrt(2x))

218+x2x \frac{2 \sqrt{18}+\sqrt{x}}{\sqrt{2 x}}

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Full solution

Q. 218+x2x \frac{2 \sqrt{18}+\sqrt{x}}{\sqrt{2 x}}
  1. Apply Quotient Rule: Apply the quotient rule of radicals to 2182\sqrt{18}. 218=29×2=2×32=622\sqrt{18} = 2\sqrt{9 \times 2} = 2 \times 3\sqrt{2} = 6\sqrt{2}.
  2. Simplify Numerator: Now, let's simplify the entire numerator. \(6\sqrt{22} + \sqrt{x})\.
  3. Simplify Denominator: Next, we'll simplify the denominator. 2x=2⋅x\sqrt{2x} = \sqrt{2} \cdot \sqrt{x}.
  4. Write Simplified Expression: Now, we'll write the simplified expression. (62+x)/(2⋅x)(6\sqrt{2} + \sqrt{x}) / (\sqrt{2} \cdot \sqrt{x}).
  5. Cannot Simplify Further: We can't simplify this further without knowing the value of xx.

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