## ValentinaT 2 years ago Simplify 4√6/√30 by rationalizing the denominator. Please show steps!

1. ValentinaT

$\frac{ 4√6 }{ \sqrt{30} }$

2. ValentinaT

Thanks.

3. kausarsalley

$\frac{ 4\sqrt6 }{ \sqrt{30} } \times \frac{ \sqrt{30} }{ \sqrt{30} }$ $\frac{ 4\sqrt6 (\sqrt{30}) }{ \sqrt{30}\times \sqrt{30} }$ $\frac{ 4\sqrt{180} }{ 30 }$ $\frac{ 24\sqrt5 }{ 30 }$ $\frac{ 4\sqrt5 }{ 5 }$

4. ValentinaT

@kausarsalley could you help me one more time?

5. kausarsalley

okay...what is the question??

6. ValentinaT

$(2\sqrt{5} + 3\sqrt{7})^2$

7. kausarsalley

okay....the simplest way to expand is to go by this... $(a+b)^2=a^2+2ab+b^2$

8. ValentinaT

It also says to justify each step? Does that mean I have to explain each step?

9. kausarsalley

using that, $(2\sqrt5+3\sqrt7)^2=(2\sqrt5)^2+2(2\sqrt5)(3\sqrt7)+(3\sqrt7)^2$

10. ValentinaT

Thanks.

11. kausarsalley

its not done with simplifying..

12. kausarsalley

or can you continue from there??

13. ValentinaT

Oh, I was just saying.

14. ValentinaT

I'm not sure what to do.

15. kausarsalley

$(2^2(\sqrt5)^2)+4\sqrt5(3\sqrt7)+(3^2(\sqrt7)^2$ $20 + 12\sqrt{35}+63$ $83+12\sqrt{35}$

16. kausarsalley

do you understand what i have done??

17. ValentinaT

I think I might, is that the final answer?

18. ValentinaT

Thanks.

19. kausarsalley

sorry for the late reply.... yw