anonymous
  • anonymous
can someone help me understand on how to simplify radicals?
Mathematics
  • Stacey Warren - Expert brainly.com
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SOLVED
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jamiebookeater
  • jamiebookeater
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saifoo.khan
  • saifoo.khan
Where are u stuck? do u have any examples?
anonymous
  • anonymous
how would I simplify 16/81 all under a square root simble?|dw:1327798829785:dw|
saifoo.khan
  • saifoo.khan
\[\sqrt{\frac{16}{81}}\]That right?

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anonymous
  • anonymous
yea!!!
saifoo.khan
  • saifoo.khan
That can we written as, \[\frac{\sqrt{16}}{\sqrt{81}}\]
saifoo.khan
  • saifoo.khan
Can you solve now?
anonymous
  • anonymous
so then it would be like 4 over 9?
anonymous
  • anonymous
is that simplified?
anonymous
  • anonymous
|dw:1327799041137:dw|
saifoo.khan
  • saifoo.khan
Yes 4/9 is correct. but How u got 4/9 ? u simplified using the square root.. So the cancel will be cancelled now.
anonymous
  • anonymous
oh that makes sense, thank you:) would you be able to help me out with a few more problems?
saifoo.khan
  • saifoo.khan
\[\sqrt{\frac{16}{81}} \to \frac{\sqrt{16}}{\sqrt{81}} \to \frac 49 \]
saifoo.khan
  • saifoo.khan
Welcome. How many do u have? i will help u as much as i can.
saifoo.khan
  • saifoo.khan
i dont have much time though.
anonymous
  • anonymous
ok, then ill ask you the ones that are more difficult than others
saifoo.khan
  • saifoo.khan
Feel free to do so.
anonymous
  • anonymous
how would i simplify |dw:1327799236709:dw|
anonymous
  • anonymous
and i also am wondering how I would solve\[2\sqrt{3}\div3\sqrt{2}\]
saifoo.khan
  • saifoo.khan
\[\sqrt{75} \text{ can be written as,} \sqrt{ 25 \times 3} \to 5 \sqrt3\]
anonymous
  • anonymous
ok i got that one thanks:)
saifoo.khan
  • saifoo.khan
So now u cann those.
saifoo.khan
  • saifoo.khan
For the second one, That is simplified, but indirectly.
anonymous
  • anonymous
one more question after the last one i posted is How do i simplify questions that have like 10 over square root 5|dw:1327799591814:dw|
saifoo.khan
  • saifoo.khan
\[\frac{10}{\sqrt5} \times \frac{\sqrt5}{\sqrt5}\]
anonymous
  • anonymous
so for the one thats simplified i would just write simplfyied?
saifoo.khan
  • saifoo.khan
Idk.. have you guys studied rationalizing?
anonymous
  • anonymous
um... i don't know
saifoo.khan
  • saifoo.khan
\[\frac{2\sqrt3}{3 \sqrt 2}\times \frac{3 \sqrt2}{3 \sqrt2}\]Now u may solve this.
anonymous
  • anonymous
i cross multiply?
saifoo.khan
  • saifoo.khan
Nope, simply multiply. You ONLY cross multiply when there's a "=" sign in between.
anonymous
  • anonymous
ah, i see
anonymous
  • anonymous
Just a nice couple of things about radicals. If a and b are numbers then \[\sqrt{ab} = \sqrt{a}\sqrt{b}\] \[\sqrt{\frac{a}{b}} = \frac{\sqrt{a}}{\sqrt{b}}\] and if n and m are any numbers, then \[n\sqrt{a} + m\sqrt{a} = (n+m)\sqrt{a}\]
anonymous
  • anonymous
should add \[b \neq 0\] for that second one..
anonymous
  • anonymous
can you help me with a problem?
anonymous
  • anonymous
what was the second one?
anonymous
  • anonymous
the second one is the fraction, one must never divide by zero. Also a and b are obviously nonnegative (unless it's an odd radical)
anonymous
  • anonymous
um can you help me with a few more questions?
anonymous
  • anonymous
? what's the problem?
anonymous
  • anonymous
how would i simplify |dw:1327800649423:dw|
saifoo.khan
  • saifoo.khan
Rationalize it, \[\frac{7}{2 \sqrt2} \times \frac{2 \sqrt2}{2 \sqrt2}\]
anonymous
  • anonymous
why do you multiply it?
saifoo.khan
  • saifoo.khan
Whenever u have a sqrt in bottom part. we always do it that way to simplify it. The method is known as rationalizing. in which we multiply and divide the fraction by the denomiator.
anonymous
  • anonymous
ok, so im stupid, so can you help me multiply that?
saifoo.khan
  • saifoo.khan
http://www.youtube.com/watch?v=gY5TvlHg4Vk
anonymous
  • anonymous
ok thanks, thats helpful :)
saifoo.khan
  • saifoo.khan
(:
saifoo.khan
  • saifoo.khan
Bye, c ya.
anonymous
  • anonymous
c ya too
anonymous
  • anonymous
on that last one it was sufficient to just multiply by \[\frac{\sqrt{2}}{\sqrt{2}}\]
anonymous
  • anonymous
which one was that?
anonymous
  • anonymous
is|dw:1327802012909:dw|
anonymous
  • anonymous
Ok, suppose you have a fraction like this \[\frac{7}{2\sqrt{2}}.\] You want to rationalise the denominator, which means - make the number on the bottom into something without roots. Now multiplying this fraction by 1 will not change it. Notice that \[1 = \frac{\sqrt{2}}{\sqrt{2}}\] and this is true for anything: something divided by itself equals 1. Therefore \[\frac{7}{2\sqrt{2}} \times \frac{\sqrt{2}}{\sqrt{2}} = \frac{7\sqrt{2}}{2(\sqrt{2})^2}\] Now the squared removes the square root and you are just left with 2: \[(\sqrt{2})^2 = 2\] So we get in the end: \[\frac{7\sqrt{2}}{4}\] and this is equal to what you started with, and the change we have made is we have rationalised the denominator.
anonymous
  • anonymous
thank you
anonymous
  • anonymous
That's wrong by the way, \[\sqrt{1} + \sqrt{1} = 2\sqrt{1}\] because there is two of them! and we know that \[\sqrt{1} = 1\] so \[\sqrt{1} + \sqrt{1} = 2\sqrt{1} = 2\]
anonymous
  • anonymous
and so the square root of 1 +the square root of 1 is 2?
anonymous
  • anonymous
yes, since the square root of 1 is 1, so it reduces to 1+1!
anonymous
  • anonymous
ah, thank you:) I have now finished my math assignment. You have helped me so much, instead of just giving me the answers you helped me understand it
anonymous
  • anonymous
no problem! Hope it's been a help

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