Is there any other way to explain how roots work?

On page 105, in Addition and Subtraction topic -- where no. 2 and 8 came from?

Please explain the Roots Drill 1-7.

Thank you so much.

Hey

I believe on page 105, numbers 2 and 8 are just for demonstration, showing that in: √2 + √2 + √8, only √2 + √2 can be added and √8 is just carried over, which gives: 2√2 + √8. Think this way (like book shows): x + x + y = 2x + y; this is because you can combine like terms.

As for Roots Drill #7: 3 √2 + 2 √8 + √32
Ok, you want to split as much as possible;
1) 3 √2 - cannot split, leave as is.

2) 2 √8 - √8 can be split into √4 * √2 - now √4 is =2; so √8 = 2√2. Therefore, 2√8 = 2 * 2√2 = 4√2

3) √32 - split this too: √4 * √4 * √2 - see that √4 = 2, therefore you get: 2 *2 * √2; OR = 4 √2

Now put together 1,2,and 3:
3 √2 + 4 √2 + 4 √2
= (3 + 4 + 4) * √2
= 11 √2

Does that help at all? You want to break; split each; then combine.

Thanks,
Jay

Thanks .. that's definitely help! ;-)