Simplifying a Root

by **Guest** Tue Nov 27, 2007 6:14 pm

This might seem like a rather simple question but I'm having some difficulty understanding a concept.

On pg. 64 of the Number Properties book it states that you can only combine a root in multiplication or division. The bottom of the page combines Sqrt(16+9)= Sqrt(25). Wouldn't this be combining a root with addition?

Thanks for the clarification

by **StaceyKoprince** Fri Nov 30, 2007 1:01 am

The "only combine with mult or div" means that if you have two separate roots connected by mult or div, you can combine that stuff under one square root sign.

So if you had SQRT16 + SQRT9, you could not combine to SQRT(16+9).
If you had SQRT16 * SQRT9, however, you could combine to SQRT(16*9).

You can still manipulate, sometimes, if you have addition or subtraction between two separate roots, as long as the terms have something in common. For example, if you have 4^2 + 4^2, you could pull a 4^2 out of each term to get 4^2(1+1) = 2*4^2.