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

Simplify and cancel terms

solution

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