Can this be simplified? ( sqrt[20] / 5 ) - ( 1 / sqrt[5] )

jdruopp

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Please help with this question.

Simplify ( sqrt[20] / 5 ) - ( 1 / sqrt[5] )

I've tried it a few times but end up with 5a sqrt15 over 5.
Is this right or can it not be simplified?
____________________________
Edited by stapel -- Reason for edit: fixing formatting
 
sqrt(20) = sqrt(4*5)

This, and the following rule, should help you: sqrt(ab) = sqrt(a)*sqrt(b)

You could also multiply the whole thing by sqrt(5)/sqrt(5), which is allowable since it does not change the expression (called a multiplicative identity).
 
if you just need to rationalize the denominator ...

\(\displaystyle \L \frac{\sqrt{20} - 1}{5\sqrt{5}} \cdot \frac{\sqrt{5}}{\sqrt{5}} = \frac{\sqrt{100} - \sqrt{5}}{25} = \frac{10 - \sqrt{5}}{25}\)
 
Sorry but I am still confused.

I can get to 2sqrt5/5 minus 1/sqrt5

then i multiplied top and bottom of second part by sqrt5 and get

2sqrt/5 minus sqrt5/5

then, sqrt5/5

Is this not right?
What am I doing wrong.
Sorry I just really dont get it
 
\(\displaystyle \L \frac{\sqrt{20} - 1}{5\sqrt{5}}\)

Rationalize the denominator by multiplying \(\displaystyle sqrt{5}\) by the numerator and denominator

As you know, \(\displaystyle \L \sqrt{x}\sqrt{x} = x\)

so you get

\(\displaystyle \L \frac{\sqrt{20} - 1}{5\sqrt{5}}\cdot \frac{\sqrt{5}}{\sqrt{5}}\)

Which gives you

\(\displaystyle \L \frac{\sqrt{20} - 1}{5\cdot 5}\cdot \frac {\sqrt{5}}{1} = \frac{\sqrt{100} -\sqrt{5}}{25}\)

Now simplify the numerator

\(\displaystyle \L \frac{\sqrt{100} -\sqrt{5}}{25} = \frac{10 -\sqrt{5}}{25}\)

I hope this helps you!
John.
 
No. because you have subtraction in the numerator: if you really wanted (2/5) to stand out... you could do this:

\(\displaystyle \L (2/5)-\frac{\sqrt{5}}{25}\)

But that is redundant...because \(\displaystyle \L (2/5)-\frac{\sqrt{5}}{25} = \frac {(2/5)25-\sqrt{5}}{25} = \frac{10 -\sqrt{5}}{25}\)

And then your back to where you started.

Cheers,
John.
 
Re: Can this be simplified? ( sqrt[20] / 5 ) - ( 1 / sqrt[5]

jdruopp said:
Simplify ( sqrt[20] / 5 ) - ( 1 / sqrt[5] )
Hmmm...I'm watching Ottawa Senators / New Jersey Devils...but:

sqrt[20] / 5 - 1 / sqrt[5]

= 2sqrt(5) / 5 - 1 / sqrt(5)

= (10 - 5) / 5sqrt(5)

= 5 / 5sqrt(5)

= 1 / sqrt(5)
 
Staple fixed his formatting, and when he did, he changed the problem.

He originally asked for: \(\displaystyle \L \frac{\sqrt{20} - 1}{5\sqrt{5}}\)
 
jwpaine said:
Staple fixed his formatting, and...changed the problem.
Students often attempt to use multi-line formatting, and to use spaces to force things to line up. The forum script strips those spaces -- from the display. But the original "formatting" is usually still visible in "edit" mode.

When the post was edited for formatting, the original multi-line formatting was converted to single-line formatting, with the apparent meaning of the displayed original spacing included.

Eliz.
 
thanks everyone for your help. i ended up getting the problem wrong, but it was my fault for trying to do the spaces in the format.
 
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