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
Examples with Solutions
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
Questions
Rationalize the denominators of the following expressions and simplify if possible.
Solutions to the Above Problems

Multiply numerator and denominator by √5
and simplify

Multiply numerator and denominator by √2  √3

Multiply numerator and denominator by (^{3}√(x^{4}))^{2}
and simplify

Multiply numerator and denominator by y  √(x^{2} + y^{2})
and simplify
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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