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Maths Exercices
Simplify radical expressions by rationalizing the denominator

Simplify radical expressions by rationalizing the denominator

To simplify radical expressions by rationalizing the denominator it will be useful to remember the following properties.

  • The multiplication property of square roots states that

  • The division property of square roots states that


Simplify

To simplify this radical expression, rewrite it with a radical in the numerator and a radical in the denominator. Then factor out any perfect squares and simplify.

   
=   Find the prime factorizations of the numerator and denominator
=   Apply the division property of square roots

To finish simplifying the expression, multiply by to rationalize the denominator.



   
=

  Simplify
=

  Simplify the denominator
=   Multiply

Simplify.