## anonymous one year ago I need help with simplifying

1. anonymous

$6a \sqrt{80b}-\sqrt{180a ^{2}b}+5a \sqrt{b}$

2. anonymous

Look at the middle term and take the prime factorization of 180

3. anonymous

Do the same for 80

4. anonymous

60 & 2 for 180 then 40&2 for 80 right?

5. anonymous

$6a\sqrt{20\cdot 2 \cdot 2 \cdot b}- \sqrt{20 \cdot 9 \cdot a\cdot a \cdot b}+5a\sqrt{b}$

6. anonymous

$60 \cdot 2 \ne 180$

7. anonymous

8. anonymous

Yes that works too :)

9. anonymous

now factor both 20's and the 9 into simpler, prime factors.

10. anonymous

10 x 2 for 20's & 3 x 3 for 9

11. anonymous

Good. $6a\sqrt{10\cdot 2\cdot 2 \cdot 2 \cdot b}- \sqrt{10 \cdot 2 \cdot 3\cdot 3 \cdot a\cdot a \cdot b}+5a\sqrt{b}$

12. anonymous

factor both 10's one more time into prime factors.

13. anonymous

5 & 2

14. anonymous

Great $$\checkmark$$ $6a\sqrt{5\cdot 2\cdot 2\cdot 2 \cdot 2 \cdot b}- \sqrt{5\cdot 2 \cdot 2 \cdot 3\cdot 3 \cdot a\cdot a \cdot b}+5a\sqrt{b}$

15. anonymous

Now for every fair of 2 numbers, 1 of them will be extracted from the square root and multiplied to the term outside the square root.

16. anonymous

pair*

17. anonymous

For example, to start you off. $6a\sqrt{5\color{blue}{\cdot 2\cdot 2}\color{red}{\cdot 2 \cdot 2} \cdot b} = 6a \cdot \color{blue}{2} \cdot \color{red}{2}\sqrt{5 \cdot b}$

18. anonymous

$48a \sqrt{5\times2timesb}-6a \sqrt{5\times2\times3 \times a \times b}+5a \sqrt{b}$

19. anonymous

Not quite. In the first part you still have a 2 left within the square root when its been paired off and pulled out already. You should just have a 5 and a b left within the square root there since they are lone pairs and cannot be pulled out. Once things are paired off, they are not rewritten within the square root. Second part, the 6a looks right, therefore the only thing that should be left within the square root should be 5 and b.

20. anonymous

ohh okay i think i got it now

21. anonymous

It should look like this: $6a\sqrt{5\color{blue}{\cdot 2\cdot 2}\color{red}{\cdot 2 \cdot 2} \cdot b} = 6a \cdot \color{blue}{2} \cdot \color{red}{2}\sqrt{5 \cdot b} = 24a\sqrt{5b}$$- \sqrt{5\cdot\color{red}{ 2 \cdot 2} \cdot \color{blue}{3\cdot 3} \cdot \color{green}{a\cdot a} \cdot b} = -6a\sqrt{5b}$

22. anonymous

yeah thats what i got

23. anonymous

|dw:1441173348642:dw|

24. anonymous

$(24a-6a)\sqrt{5b} +5a\sqrt{b}= 18a\sqrt{5b}+5a\sqrt{b}$

25. anonymous

Coool, good job!

26. anonymous

yup, and thank you for your help

27. anonymous

Np.