# 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. ### Examples

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

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

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

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

Because of the expression 3 √(x 2 ) in the denominator, multiply numerator and denominator by ( 3 √(x 2 )) 2 to obtain Simplify and cancel terms  ### 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 Rationalize the denominators of the following expressions and simplify if possible. ### Solutions to the Above Problems

1. Multiply numerator and denominator by √5 and simplify 2. Multiply numerator and denominator by √2 - √3 3. Multiply numerator and denominator by (3√(x4))2 and simplify 4. Multiply numerator and denominator by y - √(x2 + y2) and simplify 