# 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