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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