Why mathematicians move roots from the bottom to the top
In short: In algebra, having an irrational root in the denominator isn't a mistake—it's just not considered the simplest form. This video explains the mechanics of rationalising denominators to achieve mathematical clarity.
Rationalising involves moving a surd (a root) from the bottom part of a fraction, known as the denominator, to the top, or numerator. To do this, you multiply both the numerator and the denominator by that same root.
When the denominator contains an expression like a root plus another number, the process requires multiplying by the conjugate—the same terms but with the sign changed. For example, if the bottom is $\sqrt{2} + 3$, you would multiply the entire fraction by $\sqrt{2} - 3$ to simplify it.
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- Summary by Intellect · source: Rationalising The Denominator | Algebra | Maths | FuseSchool
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