## julia_copen 2 years ago Can someone help me with this radical?

1. julia_copen

$\frac{ 7 }{ \sqrt{45} }$

2. satellite73

hmmm

3. satellite73

maybe before you do that, note that $$45=9\times 5$$ and so $$\sqrt{45}=\sqrt{9\times 5}=\sqrt{9}\sqrt{5}=3\sqrt{5}$$

4. satellite73

then $\frac{ 7 }{ \sqrt{45} }=\frac{7}{3\sqrt{5}}$and now you only need to multiply top and bottom by $$\sqrt{5}$$ to remove the radical from the denominator

5. satellite73

@julia_copen you got this or you need the steps?

6. julia_copen

7. satellite73

lets start with $\frac{7}{3\sqrt{5}}$ your job is to get the radical out of the denominator, so multiply top and bottom by $$\sqrt 5$$ you get $\frac{7}{3\sqrt{5}}\times \frac{\sqrt{5}}{\sqrt{5}}=\frac{\sqrt{5}}{3\sqrt{5}\sqrt{5}}=\frac{7\sqrt{5}}{3\times 5}$

8. satellite73

typo there, meant $\frac{7}{3\sqrt{5}}\times \frac{\sqrt{5}}{\sqrt{5}}=\frac{7\sqrt{5}}{3\sqrt{5}\sqrt{5}}=\frac{7\sqrt{5}}{3\times 5}$

9. satellite73

final answer is $$\frac{7\sqrt{5}}{15}$$

10. satellite73

another quick example $\frac{4}{\sqrt{3}}=\frac{4}{\sqrt{3}}\times \frac{\sqrt{3}}{\sqrt{3}}=\frac{4\sqrt{3}}{3}$

11. julia_copen

Thanks so much! Me and my friend were having a hard time trying to understand how to break it down.

12. satellite73

yw

13. julia_copen

can you help me with another?

14. satellite73

sure

15. julia_copen

$\frac{ 1 }{ \sqrt{75z} }$

16. satellite73

is the $$z$$ inside the radical?

17. julia_copen

yes

18. satellite73

ok the idea is to see if the number is the product of some "perfect square" so in this case $$75=25\times 3$$ making $\sqrt{75}=\sqrt{25}\sqrt{3}=5\sqrt{3}$ so star with $\frac{1}{5\sqrt{3z}}$ and then multiply top and bottom by $$\sqrt{3z}$$

19. satellite73

you get $\frac{1}{5\sqrt{3z}}\times \frac{\sqrt{3z}}{\sqrt{3z}}=\frac{\sqrt{3z}}{15z}$

20. julia_copen

Okay I see. It's always difficult in the beginning for me.

21. satellite73

you will get used to it, (and then probably forget it because it is not really that useful) but in any case it gets easier

22. julia_copen

Are you still on?