anonymous 5 years ago Need help. Problem says to rationalize and simplify 6 sq rt2 divided by square root 2-3

1. anonymous

I am coming up with -12-18 square root 6 divided by 7

2. anonymous

$\frac{6\sqrt{2}}{\sqrt{2}-3}=\frac{6\sqrt{2}\times (\sqrt{2}+3)}{(\sqrt{2}-3)\times (\sqrt{2}+3)}=\frac{12+18\sqrt{2}}{-7}$

3. anonymous

Don't you need to get rid of the -7?

4. anonymous

no.

5. anonymous

why need to? -7 is a rational number. (Why do we rationalize? Because to make the denominator a rational number)

6. anonymous

understood bastax?

7. anonymous

The example in the book shows getting rid of the -7 by multiplying by -1

8. anonymous

Would my answer be correct if that was the case?

9. anonymous

sometimes authors try to bring the negative sign upwards. But keeping -7 or 7 in denominator is just the same. The answer is rationalized as long as the denominator is a rational.

10. anonymous

11. anonymous

u can bring the negative sign on the top by multiplying up and down with -1, if ur tutor taught u so.

12. anonymous

Awesome. Thank you!