Rationalize Denominators
Questions with Solutions

Grade 10 questions on how to rationalize radical 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 √(x 2 ) in the denominator, multiply numerator and denominator by ( 3 √(x 2 )) 2 to obtain
equation 9
Simplify and cancel terms
equation 10

equation 11

solution

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

More References and links

Simplify Radical Expressions - Questions with Solutions for Grade 10
High School Maths (Grades 10, 11 and 12) - Free Questions and Problems With Answers
Middle School Maths (Grades 6, 7, 8, 9) - Free Questions and Problems With Answers
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