how do you add radicals

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how do you add radicals

Mathematics
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\[6\sqrt{2*6\sqrt{8\div6\sqrt[3]{?2}}}\]
exponential equations? can anyone explain in English?
I'm not sure what the ? means so I'm going to ignore it. What you can do is set that whole expression equal to some value a. Square both sides. Then square them again. Then cube both sides. Now all the radicals are gone and you will have integer exponents on both sides. you should have a^12 on the right. Take the whole thing on the left and raise it to the 1/12 power. That is the value of the expression.

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Other answers:

i can help you with the steps if you need. Is this what you wanted; a simplified expression?
simplify
allright did my post make sense to you?
not really. I have no Idea what I'm doing
ok ill try to type it in the equation editor.
k
\[6\sqrt{2*6\sqrt{8\div \sqrt[3]{2}}}=a\] square both sides \[36*2*6\sqrt{8\div6\sqrt[3]{2}}=a ^{2}\] square both sides again \[36^{2}*2^{2}*6^{2}*8\div6\sqrt[3]{2}=a ^{4}\] cube both sides \[36^{6}*2^{6}*6^{6}*8^{3}/(6^{3}*2)=a^{12}\]
now just take everything to the 1/12 power
and you've simplified to just one rational exponent
ok?
i kind of get it
you can simplify it even further than i said by subtracting exponents
k
I have trouble with the exponents
do you know x^a/x^b=x^(a-b)
no
if you have two exponential terms with the same base when you multiply them you can add the exponents and when you divide you can subtract the exponents
ok
x^a*x^b=x^(a+b)
\[\left(6\sqrt{2*6\sqrt{\frac{8}{6\sqrt[3]{2}}}}\right)^2\text{-$>$}\left(144\ 2^{5/6} \sqrt{3}\right)^2\text{-$>$}124416\ 2^{2/3} \]\[\sqrt[4]{124416\ 2^{2/3}}= 12\ 2^{5/12} 3^{1/4} \]
Took the original problem expression and deleted the ? mark. Squared the expression and simplified. Squared the result and simplified. Took the fourth root of the last expression to offset the two squares and simplified. Would never attempt this thing without Mathematica executing the book keeping so to speak.
robtobey and my answers are equivalent
Think i'll go talk to my teacher tomorrow. I don't understand it. Thank for your help though
depends on what you think is simplest i geuss though. Allright good luck
To verify the result, Mathematica reported "True" regarding the assertion that the following expression was valid:\[6\sqrt{2*6\sqrt{\frac{8}{6\sqrt[3]{2}}}}\text{=}12\ 2^{5/12} 3^{1/4} \]

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