# Learn to Multiply and Divide Roots – Lesson 141 of Doodles Do Algebra

Today your child will learn to multiply and divide roots. The basic concept is the same as multiplying and dividing in algebra: you can multiply like terms. Remember when we talked about laying the apples, oranges, and raisins out on the kitchen table and having your child group them into like terms as a way to show him that you really cannot combine “terms” (or items) that are in different categories? It was a long time ago, if you have been working your way through this course, so it may be that you need to remind your child of the concept. This is where hands-on and real-life examples like the fruits at the kitchen table come in handy. Those types of memories are generally “sticky”. “Sticky” is a term I first came across in marketing classes, but it really applies to teaching your child just as well, and perhaps better. If you can associate a learned concept with a hands-on activity, all you have to do in the future is say, “remember when we sat at the table and grouped the apples and the oranges into piles and talked about grouping like terms – and then you ate the raisins?” That is a “sticky” memory and the more of those you can make for your child, the better he will retain what he learns.

Back to the algebra lesson. The explanation on the worksheet for today is quite detailed and walks your child (or you) through the process of multiplying or dividing monomials with roots in them. The only tricky bit is dividing or multiplying two monomials that have roots of different order (like a square root times a cube root). Then you have go back to the tools your child learned in lesson 137: x to the “a”th power times x to the “b”the power is x to the “a+b”th power. So as an example, the square root of 2 times the cube root of 2 is the same as 2 to the 1/2 power times 2 to the 1/3 power, which is 2 to the (1/2 plus 1/3) power, or 2 to the 5/6 power. Not hard, right?

1. $6c^2d$ times the square root of x
4. 3 times 2 to the 1/6 power (because you end up with $2^(1/2)$ divided by $2^(1/3)$ which is the same as $2^(1/2)$ multiplied by $2^(-1/3)$ so that is (by way of the rule your child learned in lesson 137) $2^((1/2)-(1/3))=2^((3/6)-(2/6))=2^(1/6)$