Rationalizing a denominator sounds like a rule invented to torment you. It is not. It rests on one honest idea: any nonzero thing divided by itself equals 1, and multiplying by 1 changes how a number looks but never what it is. Watch the value on the left as you step — it lands on the same point every single line. All you are choosing is which disguised 1 to multiply by, and the answer depends on what kind of denominator you are facing.
Why the multiplier works
Every line equals—
Same value, friendlier shape
DENOMINATOR √n2 – 60
Radical below
Radical above
Rationalizing, one line at a timepick a denominator type, then an example