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Grade 11 Pre-Calculus Mathematics (30S)
Develop algebraic reasoning and number sense
2. Solve problems involving operations on radicals and radical expressions with numerical and variable radicands
2.7 Dividing radicals
Dividing Radicals
Master dividing radicals using the quotient rule and learn how to rationalize the denominator so every radical expression ends up in simplest form.
What You'll Learn
Dividing radicals means combining the quotient rule, which lets you write one radical over another as a single radical of the quotient
A denominator that still contains a radical is not considered simplified, so it must be rationalized
To rationalize a single-term radical denominator, multiply top and bottom by a radical that completes a perfect power
To rationalize a two-term denominator, multiply top and bottom by its conjugate to clear the radical using a difference of squares
Always simplify the resulting radicals fully and reduce any common factors left in the fraction
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