Can someone help me with this radical?

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Can someone help me with this radical?

Mathematics
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\[\frac{ 7 }{ \sqrt{45} }\]
hmmm
maybe before you do that, note that \(45=9\times 5\) and so \(\sqrt{45}=\sqrt{9\times 5}=\sqrt{9}\sqrt{5}=3\sqrt{5}\)

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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
@julia_copen you got this or you need the steps?
Steps please.
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 \[\frac{7}{3\sqrt{5}}\times \frac{\sqrt{5}}{\sqrt{5}}=\frac{\sqrt{5}}{3\sqrt{5}\sqrt{5}}=\frac{7\sqrt{5}}{3\times 5}\]
typo there, meant \[\frac{7}{3\sqrt{5}}\times \frac{\sqrt{5}}{\sqrt{5}}=\frac{7\sqrt{5}}{3\sqrt{5}\sqrt{5}}=\frac{7\sqrt{5}}{3\times 5}\]
final answer is \(\frac{7\sqrt{5}}{15}\)
another quick example \[\frac{4}{\sqrt{3}}=\frac{4}{\sqrt{3}}\times \frac{\sqrt{3}}{\sqrt{3}}=\frac{4\sqrt{3}}{3}\]
Thanks so much! Me and my friend were having a hard time trying to understand how to break it down.
yw
can you help me with another?
sure
\[\frac{ 1 }{ \sqrt{75z} }\]
is the \(z\) inside the radical?
yes
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 \(\sqrt{3z}\)
you get \[\frac{1}{5\sqrt{3z}}\times \frac{\sqrt{3z}}{\sqrt{3z}}=\frac{\sqrt{3z}}{15z}\]
Okay I see. It's always difficult in the beginning for me.
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
Are you still on?

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