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Mathematics 8 Online
OpenStudy (anonymous):

math fun fun

OpenStudy (anonymous):

OpenStudy (danjs):

Break down each of those numbers into their prime factorization , for each of the roots

OpenStudy (anonymous):

can you help me

OpenStudy (anonymous):

243‾√

OpenStudy (anonymous):

i get that

OpenStudy (danjs):

\[\sqrt{18}={\sqrt{3*3*2}}\] for the first one

OpenStudy (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

OpenStudy (anonymous):

18

OpenStudy (danjs):

so 18 = 3^2*2 \[\sqrt{18}=\sqrt{3^2*2}=\sqrt{3^2}*\sqrt{2} = 3\sqrt{2}\]

OpenStudy (danjs):

you see how that works?

OpenStudy (anonymous):

BUT HOW CAN I PUG THAT TOT HIS

OpenStudy (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

OpenStudy (anonymous):

=(

OpenStudy (danjs):

12 = 6 * 2 = 3 * 2 * 2 = 3 * 2^2 8 = 2 * 4 = 2 * 2 * 2 = 2 * 2^2 so you have this \[\large \sqrt{2*3^2}+\sqrt{3 * 2^2} + \sqrt{2*2^2}\]

OpenStudy (danjs):

recall that the square root of a product is the product of two square roots ... \[\sqrt{a*b} = \sqrt{a}*\sqrt{b}\]

OpenStudy (anonymous):

18 12 8

OpenStudy (danjs):

and the square root is the same as rasing to the (1/2) power \[\sqrt{x}=x^{1/2}\]

OpenStudy (anonymous):

-(((((((

OpenStudy (anonymous):

look at my private message

OpenStudy (danjs):

so x^2 to the 1/2 power becomes x^(2/2) = x

OpenStudy (danjs):

those are the things you have to remember... so you get \[\large \sqrt{2*3^2}+\sqrt{3 * 2^2} + \sqrt{2*2^2} = 3\sqrt{2}+2\sqrt{3}+2\sqrt{2}\]

OpenStudy (anonymous):

OpenStudy (danjs):

you can combine the terms with the same things under their roots...

OpenStudy (danjs):

so 5 root 2 plus 2 root 3

OpenStudy (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

OpenStudy (danjs):

after a few practice probs, this prob will take you 30 seconds maybe

OpenStudy (danjs):

\[2\sqrt{3}+5\sqrt{2}\]

OpenStudy (anonymous):

that the final answer?

OpenStudy (danjs):

yes, simplest form, hope you see how it breaks down

OpenStudy (anonymous):

thanks you new post

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