Rationalizing the denominator
Rationalize the denominator — remove the surd from the denominator and simplify the answer.
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To rationalize the denominator means to rewrite a fraction so that there is no surd in the denominator. We multiply the top and the bottom of 6/√3 by √3: the denominator becomes √3 · √3 = 3 and we get 6√3/3 = 2√3. Multiplying the top and the bottom by the same number does not change the value of the fraction.
What does this generator do?
On the easy level there is one root in the denominator (6/√3). On the medium level there is a number in front of it, or a root in the numerator too (10/(3√5), √3/√8). On the hard level the denominator has two terms, like √5 − √2 or √7 + 2 — you multiply top and bottom by the conjugate (the same terms with the opposite sign).
How to use it
1) With one root in the denominator, multiply the top and the bottom by the same root. 2) With two terms √a − b, multiply top and bottom by the conjugate √a + b; in the denominator use (x − y)(x + y) = x² − y². 3) Cancel the answer. Write the numerator and the denominator in the boxes; if the denominator is 1, leave it empty.