Question

Can someone help me with this radical?

Answer 1

\[\frac{ 7 }{ \sqrt{45} }\]

Answer 2

hmmm

Answer 3

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

Answer 4

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

Answer 5

@julia_copen you got this or you need the steps?

Answer 6

Steps please.

Answer 7

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
\[\frac{7}{3\sqrt{5}}\times \frac{\sqrt{5}}{\sqrt{5}}=\frac{\sqrt{5}}{3\sqrt{5}\sqrt{5}}=\frac{7\sqrt{5}}{3\times 5}\]

Answer 8

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

Answer 9

final answer is \(\frac{7\sqrt{5}}{15}\)

Answer 10

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

Answer 11

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

Answer 12

yw

Answer 13

can you help me with another?

Answer 14

sure

Answer 15

\[\frac{ 1 }{ \sqrt{75z} }\]

Answer 16

is the \(z\) inside the radical?

Answer 17

yes

Answer 18

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 \(\sqrt{3z}\)

Answer 19

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

Answer 20

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

Answer 21

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

Answer 22

Are you still on?