Simplifying expressions with radicals

[PurpleAnnie]

I'm new at this. . .so. . .

(first,is there an easy way to type in a square root (3rd root, 4th root, etc.)??

Problem:

square root of 2/5 + square root of 40 + square root of 10

Here's how I started:

square root of 2 over square root of 5; eliminate radical in denominator by multiplying both numerator and denominator by square root of 5; .5 square root of 5 + 2 square root of 10 + square root of 10. . .

I think the answer is (3.5 * square root of 10). . .but my book has a different answer (16 square root of ten over 5)

Help!

PurpleAnnie

 

[Denis]

square root of 2/5 + square root of 40 + square root of 10

.5 square root of 5 + 2 square root of 10 + square root of 10. . .

Type 'em this way: sqrt(2/5) + sqrt(40) + sqrt(10)

Explain where/how you got that .5 !!

Did you know that sqrt(10) = sqrt(5) * sqrt(2) ?

 

[PurpleAnnie]

Here's the problem again:

sqrt(2/5) + sqrt(40) + sqrt(10)

yes, I know that sqrt(10) is sqrt(2) * sqrt(5)

When I multiplied numerator and denominator by sqrt(5) to remove radical in denominator, I got
sqrt(2)*sqrt(5) or sqrt(10)/5--oh, oh, I see my problem here...I was thinking 1/2 rather than 1/5..

but that still leaves my answer as sqrt(10)/5 + 2*sqrt(10) + sqrt(10) or sqrt(10)/5 + 3*sqrt(10)

How do I get to THE answer...16 * sqrt(10)/5????

 

[Loren]

Type "\sqrt{\frac{2}{5}}", then hi-lite it and select the "tex" button at upper right of this text box and you get... \(\displaystyle \sqrt{\frac{2}{5}}\)

Also, get started on LaTeX by consulting the "Forum Help" drop down menu at the very top of the page.

 

[PurpleAnnie]

I have a lot to learn about using this site most efficiently, but. . .

I'll have to study the forum. . .but I couldn't get tex to work. I even copied the notation in the last response and tried it. .no luck. And right now I don't have time to figure all that out. . .and I still can't understand how to get the answer to

sqrt(2/5) + sqrt(40) + sqrt(10) =

sqrt(2)*sqrt(5)/sqrt(5)*sqrt(5) + sqrt(4) * sqrt (10) + sqrt(10) =

sqrt(10)/5 + 2*sqrt(10) + sqrt(10) =

sqrt(10)/5 + 3*sqrt(10) That's where I ended. I still can't see the [16*sqrt(10)]/5

PurpleAnnie...about to give up.

Help.

 

[Loren]

sqrt(2/5) + sqrt(40) + sqrt(10)
\(\displaystyle \sqrt{\frac{2}{5}}=\frac{\sqrt2}{\sqrt5}=\frac{\sqrt2}{\sqrt5}\cdot \frac{\sqrt5}{\sqrt5}=\frac{\sqrt{10}}{5}\)

\(\displaystyle \sqrt{40}=\sqrt{4\cdot 10} = 2\sqrt{10}\)

This gives you...
\(\displaystyle \frac{1}{5}\sqrt{10} + 2\sqrt{10} + \sqrt{10}=(\frac{1}{5}+2+1)\sqrt{10}=\) you finish.

Re your sqrt(10)/5 + 3*sqrt(10)....
\(\displaystyle \frac{\sqrt{10}}{5}+3\sqrt{10}=\frac{\sqrt{10}}{5}+\frac{15\sqrt{10}}{5}=\frac{1\sqrt{10}+15\sqrt{10}}{5}=\frac{16\sqrt{10}}{5}\)

 

[PurpleAnnie]

I don't know if my last note posted. . .but I had figured this out overnight. I think I was just up too late and too tired. But it's reassuring to see that I followed correct procedures. It actually was quite a simple problem. . .once I remembered how to combine terms. Duh. Thanks to all of you for your help.

As for using the LaTeX...I may never figure that out. It's so confusing to me.
Does it matter that I'm working on an older Mac--an iBook G4??

Cheerio for now,
PurpleAnnie

 

[Loren]

I don't think it matters.