Question

how do you add radicals

Answer 1

\[6\sqrt{2*6\sqrt{8\div6\sqrt[3]{?2}}}\]

Answer 2

exponential equations? can anyone explain in English?

Answer 3

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.

Answer 4

i can help you with the steps if you need. Is this what you wanted; a simplified expression?

Answer 5

simplify

Answer 6

allright did my post make sense to you?

Answer 7

not really. I have no Idea what I'm doing

Answer 8

ok ill try to type it in the equation editor.

Answer 9

k

Answer 10

\[6\sqrt{2*6\sqrt{8\div \sqrt[3]{2}}}=a\]
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
\[36^{6}*2^{6}*6^{6}*8^{3}/(6^{3}*2)=a^{12}\]

Answer 11

now just take everything to the 1/12 power

Answer 12

and you've simplified to just one rational exponent

Answer 13

ok?

Answer 14

i kind of get it

Answer 15

you can simplify it even further than i said by subtracting exponents

Answer 16

k

Answer 17

I have trouble with the exponents

Answer 18

do you know x^a/x^b=x^(a-b)

Answer 19

no

Answer 20

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

Answer 21

ok

Answer 22

x^a*x^b=x^(a+b)

Answer 23

\[\left(6\sqrt{2*6\sqrt{\frac{8}{6\sqrt[3]{2}}}}\right)^2\text{-$>$}\left(144\ 2^{5/6} \sqrt{3}\right)^2\text{-$>$}124416\ 2^{2/3} \]\[\sqrt[4]{124416\ 2^{2/3}}= 12\ 2^{5/12} 3^{1/4} \]

Answer 24

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.

Answer 25

robtobey and my answers are equivalent

Answer 26

Think i'll go talk to my teacher tomorrow. I don't understand it. Thank for your help though

Answer 27

depends on what you think is simplest i geuss though. Allright good luck

Answer 28

To verify the result, Mathematica reported "True" regarding the assertion that the following expression was valid:\[6\sqrt{2*6\sqrt{\frac{8}{6\sqrt[3]{2}}}}\text{=}12\ 2^{5/12} 3^{1/4} \]