Rationalize Denominators of Radical Expressions
Questions with Solutions for Grade 10

Grade 10 questions on how to rationalize radicals expressions with solutions are presented.

To rationalize radical expressions with denominators is to express the denominator without radicals

The following identities may be used to rationalize denominators of rational expressions.

equation 1


Examples


Rationalize the denominators of the following expressions and simplify if possible.

equation 2

Solution

Because of √2 in the denominator, multiply numerator and denominator by √2 and simplify

equation 3


equation 4

Solution

Because of
3√x in the denominator, multiply numerator and denominator by (3√x)2 and simplify

equation 5


equation 6

Solution

Because of the expression √3 - √2 in the denominator, multiply numerator and denominator by its conjugate √3 + √2 to obtain

equation 7


equation 8

Solution

Because of the expression
3√(x2) in the denominator, multiply numerator and denominator by (3√(x2))2 to obtain

equation 9

Simplify and cancel terms

equation 10


equation 11

Solution

Because of the expression y + √(x
2+y2) in the denominator, multiply numerator and denominator by its conjugate y - √(x2 + y2) to obtain

equation 12


Questions With Answers


    Rationalize the denominators of the following expressions and simplify if possible.
    equation 13

    Solutions to the Above Problems

    1. Multiply numerator and denominator by √5

      equation 14

      and simplify

      equation 15
    2. Multiply numerator and denominator by √2 - √3

      equation 16
    3. Multiply numerator and denominator by (3√(x4))2

      equation 17

      and simplify

      equation 18


    4. Multiply numerator and denominator by y - √(x2 + y2)

      equation 19

      and simplify

      equation 20


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