## miah 2 years ago Help

1. miah

$10\sqrt[4]{6} + 4\sqrt[3]{6} - 9\sqrt[3]{6} - 3\sqrt[4]{6}$

2. miah

@jim_thompson5910

3. jim_thompson5910

What are the common terms here

4. miah

$10\sqrt[4]{6} and 3\sqrt[4]{6}$

5. miah

$4\sqrt[3]{6} and 9\sqrt[3]{6}$

6. jim_thompson5910

good, so combine those pairs of like terms

7. jim_thompson5910

for example, $$\large 10\sqrt[4]{6}$$ and $$\large -3\sqrt[4]{6}$$ combine to $$\large 10\sqrt[4]{6} -3\sqrt[4]{6}$$ $$\large (10 -3)\sqrt[4]{6}$$ $$\large 7\sqrt[4]{6}$$

8. jim_thompson5910

how about the other pair of terms? what do they combine to?

9. miah

$-5\sqrt[3]{6}$

10. miah

so the answer is $7\sqrt[4]{6} - 5\sqrt[3]{6}$

11. miah

@jim_thompson5910

12. jim_thompson5910

good you got it

13. miah

14. miah

15. jim_thompson5910

you want to simplify this?

16. miah

Well it has what i said then my bf said 2√6 and thats also an answer choice.

17. jim_thompson5910

oh no it's $7\sqrt[4]{6} - 5\sqrt[3]{6}$ like you said

18. miah

I have another if you dont mind @jim_thompson5910

19. miah

$\sqrt{10} (4-\sqrt{5}) + \sqrt{8} (\sqrt{5}+2)$

20. jim_thompson5910

$\Large \sqrt{10} (4-\sqrt{5}) + \sqrt{8} (\sqrt{5}+2)$ $\Large \sqrt{10} (4)-\sqrt{10} \sqrt{5} + \sqrt{8}\sqrt{5}+\sqrt{8}(2)$ $\Large 4\sqrt{10}-\sqrt{10*5} + \sqrt{8*5}+2\sqrt{8}$ $\Large 4\sqrt{10}-\sqrt{50} + \sqrt{40}+2\sqrt{8}$ $\Large 4\sqrt{10}-\sqrt{25*2} + \sqrt{4*10}+2\sqrt{4*2}$ $\Large 4\sqrt{10}-\sqrt{25}*\sqrt{2} + \sqrt{4}*\sqrt{10}+2\sqrt{4}\sqrt{2}$ $\Large 4\sqrt{10}-5\sqrt{2} + 2\sqrt{10}+2*2\sqrt{2}$ $\Large 4\sqrt{10}-5\sqrt{2} + 2\sqrt{10}+4\sqrt{2}$ $\Large 6\sqrt{10}-\sqrt{2}$

21. miah

Thank youuu!

22. jim_thompson5910

yw

23. miah

$\frac{ 2 }{ 6-\sqrt{3} }$

24. miah

Last one i Promise. lol

25. miah

@jim_thompson5910

26. jim_thompson5910

multiply top and bottom by $$\Large 6+\sqrt{3}$$ and tell me what you get

27. miah

12 over √ 3

28. jim_thompson5910

no you should get this

29. jim_thompson5910

$\Large \frac{ 2 }{ 6-\sqrt{3} }$ $\Large \frac{ 2(6+\sqrt{3}) }{ (6-\sqrt{3})(6+\sqrt{3}) }$ $\Large \frac{ 2(6+\sqrt{3}) }{ 6^2 - \left(\sqrt{3}\right)^2 }$ $\Large \frac{ 2(6+\sqrt{3}) }{ 36 - 3 }$ $\Large \frac{ 2(6+\sqrt{3}) }{ 33 }$ $\Large \frac{ 12+2\sqrt{3} }{ 33 }$

30. miah

Thanks!

31. jim_thompson5910

np