The Power of the Conjugate!

Stuck with a radical in the denominator? What if I told you there's a magic 'conjugate' that can make it disappear?

Subject: algebra • Classes: 6–12 • Difficulty: intermediate (9-10)

The Trick

To rationalize a denominator containing a binomial with a square root (e.g., $a + \sqrt{b}$), multiply both the numerator and denominator by its conjugate, which is $a - \sqrt{b}$. Why does this work? Because $(a + \sqrt{b})(a - \sqrt{b}) = a^2 - (\sqrt{b})^2 = a^2 - b$, eliminating the square root in the denominator.

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