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 \( \sqrt 2 \) in the denominator, multiply numerator and denominator by \( \sqrt 2 \) and simplify
solution
Because of \( \sqrt[3]{x} \) in the denominator, multiply the numerator and denominator by \( \left( \sqrt[3]{x} \right)^2 \) and simplify.
solution
Because of the expression \( \sqrt{3} - \sqrt{2} \) in the denominator, multiply the numerator and denominator by the conjugate of \( \sqrt{3} - \sqrt{2} \) which is \( \sqrt{3} + \sqrt{2} \) to obtain:
solution
Because of the expression \( \sqrt[3]{x^2} \) in the denominator, multiply the numerator and denominator by \( \left( \sqrt[3]{x^2} \right)^2 \) to obtain
Simplify and cancel terms
solution
Because of the expression \( y + \sqrt{x^2 + y^2} \) in the denominator, multiply numerator and denominator by its conjugate \( y - \sqrt{x^2 + y^2} \) to obtain
Questions
Rationalize the denominators of the following expressions and simplify if possible.
Solutions to the Above Problems
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Multiply numerator and denominator by \( \sqrt 5 \)
and simplify
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Multiply numerator and denominator by \( \sqrt 2 - \sqrt 3 \)
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Multiply numerator and denominator by \( \left( \sqrt[3]{x^4} \right)^2 \)
and simplify
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Multiply numerator and denominator by \( y - \sqrt{x^2 + y^2} \)
and simplify
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