anonymous
  • anonymous
math fun fun
Mathematics
  • Stacey Warren - Expert brainly.com
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SOLVED
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jamiebookeater
  • jamiebookeater
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anonymous
  • anonymous
DanJS
  • DanJS
Break down each of those numbers into their prime factorization , for each of the roots
anonymous
  • anonymous
can you help me

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anonymous
  • anonymous
243‾√
anonymous
  • anonymous
i get that
DanJS
  • DanJS
\[\sqrt{18}={\sqrt{3*3*2}}\] for the first one
DanJS
  • DanJS
If an even number, i would start by pulling out as many 2's as possible, for that 18, you get 2*9, then 9 is 3*3
anonymous
  • anonymous
18
DanJS
  • DanJS
so 18 = 3^2*2 \[\sqrt{18}=\sqrt{3^2*2}=\sqrt{3^2}*\sqrt{2} = 3\sqrt{2}\]
DanJS
  • DanJS
you see how that works?
anonymous
  • anonymous
BUT HOW CAN I PUG THAT TOT HIS
DanJS
  • DanJS
You have to do that for all three of those roots, the only way you can combine them after that is if they are the same things under the roots
anonymous
  • anonymous
=(
DanJS
  • DanJS
12 = 6 * 2 = 3 * 2 * 2 = 3 * 2^2 8 = 2 * 4 = 2 * 2 * 2 = 2 * 2^2 so you have this \[\large \sqrt{2*3^2}+\sqrt{3 * 2^2} + \sqrt{2*2^2}\]
DanJS
  • DanJS
recall that the square root of a product is the product of two square roots ... \[\sqrt{a*b} = \sqrt{a}*\sqrt{b}\]
anonymous
  • anonymous
18 12 8
DanJS
  • DanJS
and the square root is the same as rasing to the (1/2) power \[\sqrt{x}=x^{1/2}\]
anonymous
  • anonymous
-(((((((
anonymous
  • anonymous
look at my private message
DanJS
  • DanJS
so x^2 to the 1/2 power becomes x^(2/2) = x
DanJS
  • DanJS
those are the things you have to remember... so you get \[\large \sqrt{2*3^2}+\sqrt{3 * 2^2} + \sqrt{2*2^2} = 3\sqrt{2}+2\sqrt{3}+2\sqrt{2}\]
anonymous
  • anonymous
DanJS
  • DanJS
you can combine the terms with the same things under their roots...
DanJS
  • DanJS
so 5 root 2 plus 2 root 3
DanJS
  • DanJS
\[(3+2)\sqrt{2}+2\sqrt{3}\] thats it... you just have to know the root properties and how to break each number into smaller factors
DanJS
  • DanJS
after a few practice probs, this prob will take you 30 seconds maybe
DanJS
  • DanJS
\[2\sqrt{3}+5\sqrt{2}\]
anonymous
  • anonymous
that the final answer?
DanJS
  • DanJS
yes, simplest form, hope you see how it breaks down
anonymous
  • anonymous
thanks you new post

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