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Rationalizing the denominator worksheets Grade 10

Remove roots from the denominator by multiplying by the root or the conjugate.

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Free · Worked example · 34 problems · Answer key · US Letter

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How to do it

Multiply the top and the bottom by the root, or by the conjugate: for 3 − √5, use 3 + √5. Leave no root in the denominator.

105=10⋅55⋅5=1055=25\dfrac{10}{\sqrt{5}} = \dfrac{10 \cdot \sqrt{5}}{\sqrt{5} \cdot \sqrt{5}} = \dfrac{10\sqrt{5}}{5} = 2\sqrt{5}multiply the top and the bottom by √5, then reduce

Example problems

  1. 365+7=\dfrac{36}{5 + \sqrt{7}} =
  2. 35=\dfrac{3}{\sqrt{5}} =
  3. 1211=\dfrac{12}{\sqrt{11}} =
  4. 336−3=\dfrac{33}{6 - \sqrt{3}} =

Exponents, radicals and complex numbers

  1. Zero and negative exponents
  2. Rational exponents
  3. Converting between radicals and rational exponents
  4. Exponent rules with rational exponents
  5. Simplifying cube roots and higher roots
  6. Rationalizing the denominator
  7. Solving radical equations
  8. Imaginary numbers and powers of i
  9. Adding, subtracting and multiplying complex numbers
  10. Dividing complex numbers