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Write a factor that you can use to rationalize the denominator of 
(sqrt2)/(sqrt5-8)

Write a factor that you can use to rationalize the denominator of \newline258\frac{\sqrt{2}}{\sqrt{5}-8}

Full solution

Q. Write a factor that you can use to rationalize the denominator of \newline258\frac{\sqrt{2}}{\sqrt{5}-8}
  1. Recognize form of denominator: Step 11: Recognize the form of the denominator.\newlineThe denominator is 58\sqrt{5} - 8, which is a binomial with a square root.
  2. Choose conjugate for rationalization: Step 22: Choose the conjugate of the denominator to rationalize it.\newlineThe conjugate of 58\sqrt{5} - 8 is 5+8\sqrt{5} + 8. Multiplying by the conjugate will eliminate the square root from the denominator.
  3. Write factor for rationalization: Step 33: Write the factor used for rationalization.\newlineThe factor used to rationalize the denominator is 5+8\sqrt{5} + 8.

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