math fun fun
Break down each of those numbers into their prime factorization , for each of the roots
can you help me
243‾√
i get that
\[\sqrt{18}={\sqrt{3*3*2}}\] for the first one
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
18
so 18 = 3^2*2 \[\sqrt{18}=\sqrt{3^2*2}=\sqrt{3^2}*\sqrt{2} = 3\sqrt{2}\]
you see how that works?
BUT HOW CAN I PUG THAT TOT HIS
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
=(
12 = 6 * 2 = 3 * 2 * 2 = 3 * 2^2 8 = 2 * 4 = 2 * 2 * 2 = 2 * 2^2 so you have this \[\large \sqrt{2*3^2}+\sqrt{3 * 2^2} + \sqrt{2*2^2}\]
recall that the square root of a product is the product of two square roots ... \[\sqrt{a*b} = \sqrt{a}*\sqrt{b}\]
18 12 8
and the square root is the same as rasing to the (1/2) power \[\sqrt{x}=x^{1/2}\]
-(((((((
look at my private message
so x^2 to the 1/2 power becomes x^(2/2) = x
those are the things you have to remember... so you get \[\large \sqrt{2*3^2}+\sqrt{3 * 2^2} + \sqrt{2*2^2} = 3\sqrt{2}+2\sqrt{3}+2\sqrt{2}\]
you can combine the terms with the same things under their roots...
so 5 root 2 plus 2 root 3
\[(3+2)\sqrt{2}+2\sqrt{3}\] thats it... you just have to know the root properties and how to break each number into smaller factors
after a few practice probs, this prob will take you 30 seconds maybe
\[2\sqrt{3}+5\sqrt{2}\]
that the final answer?
yes, simplest form, hope you see how it breaks down
thanks you new post
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