Algebrarules.com

The most useful rules of basic algebra,
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Howdy! Here are a few very handy rules of algebra. These basic rules are useful for everything from figuring out your gas mileage to acing your next math test — or even solving equations from the far reaches of theoretical physics. Happy calculating!



Algebra Rule 20


The root of a multiplication equals the product of the roots of its factors

```\sqrt[n]{ab} = \sqrt[n]{a}\sqrt[n]{b}```
Description:

If ``x = \sqrt{a}`` and ``y = \sqrt{b}`` then ``\sqrt{ab} = \sqrt{x^2*y^2}`` If we write out the multiplication, this turns into ``\sqrt{x*x*y*y}``. Thanks to the commutative property of multiplication, we can rearrange the Xs and Ys and get ``\sqrt{x*y*x*y} = \sqrt{(x*y)(x*y)} = \sqrt{(x*y)^2} = x*y = \sqrt{a}*\sqrt{b}``

```\sqrt{4*9} = \sqrt{36} = 6 = 2*3 = \sqrt{4}*\sqrt{9}```
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Algebra rules is a project by two of the folks who run The Autodidacts.

A couple of autodidact math enthusiasts, we were looking for all the rules of basic algebra concisely presented in one place. We couldn’t find such a place, so we made Algebrarules.com

These simple rules — applied with a pinch of imagination and a dash of arithmetic — can divide, conquer, and solve just about any practical algebra problem.

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