Question

rationalize denominators to simplify radical expressions
4th root 2/4th root 5

Answer 1

\[\frac{ \sqrt[4]{2} }{ \sqrt[4]{5} }\]

Answer 2

These suck.

It's probably easier to turn things into fractional exponents first \[\large \frac{ 2^{1/4} }{ 5^{1/4} }\]
You have to multiply the top and bottom by something that'll make the exponent on the 5 into a 1.
\[\Large \frac{ 2^{1/4} }{ 5^{1/4} }*\frac{ 5^{3/4} }{ 5^{3/4}}\] why 3/4? because 1/4 + 3/4 is...

Answer 3

1

Answer 4

\[\Large \frac{ 2^{1/4} }{ 5^{1/4} }*\frac{ 5^{3/4} }{ 5^{3/4}} = \frac{ 2^{1/4} *5^{3/4}}{ 5 }\]

Answer 5

is it \[\frac{ \sqrt[4]{250} }{ 5 }\]

Answer 6

Now turn the 1/4 exponents back into 4th root symbols\[\Large \frac{ \sqrt[4]{2} * \sqrt[4]{5^{3}}}{ 5 }=\]

Answer 7

okay so the answer is \[\frac{ \sqrt[4]{250} }{5 }\]

Answer 8

can you help me with another problem?

Answer 9

Okay

Answer 10

\[(\sqrt{y}+\sqrt{2})(\sqrt{y}-7\sqrt{2})\]

Answer 11

Expand it like you would any expression like that.

Answer 12

what?

Answer 13

Like any expression of that form eg. (x+2)(x-6)

Answer 14

ohh distribute

Answer 15

i forgot how to distribute radicals

Answer 16

Remember drawing the lines, from each term to each other term in the parentheses... so you don't forget anything

Answer 17

yes i remember that part