Question

HELP ASAP (MEDAL + FAN) (PIC) Distribute and simplify the radicals below.

Answer 1

Here

Answer 2

hi owletgggggggggggggggggggggggggg

Answer 3

It should simplify to
\[(2\sqrt{2}+\sqrt{3})(2\sqrt{3}-\sqrt{2})\]
Now distribute.

Answer 4

I DONT KNOW HOW TO DISTRIBUTE RADICALS @AlwaystheBookworm

Answer 5

http://www.mesacc.edu/~scotz47781/mat120/notes/radicals/multiplying/more_than_one_term/mult_rad_more_than_1.html

Answer 6

I'm horrible at distributing radicals sorry

Answer 7

Ok, so we are going to FOIL this: (front, out, inside, last)

Answer 8

when we multiply the radicals, we are going to multiply them from the inside
so for example : \[\sqrt{8 \times 12}\]

Answer 9

So lets do this :)
F: \[\sqrt{8 \times 12} = \sqrt{96}\]
O: \[\sqrt{8 \times 2}= \sqrt{16}\]
I: \[\sqrt{3 \times 12}= \sqrt{36}\]
L: \[\sqrt{3 \times 2}= \sqrt{6}\]
So now lets put them in order:
\[\sqrt{96}-\sqrt{16}+\sqrt{36}-\sqrt{6}\]
So we're done distributing this =D

Answer 10

Notice how some of these can be squared into a number like \[\sqrt{16} and \sqrt{36}\]
\[\sqrt{16 } =4\]
\[\sqrt{36}= 6\]

Answer 11

So let's do that in the equation :)
\[\sqrt{96}-4+6-\sqrt{6}\]
Let's add -4 and 6 to make it a bit cleaner
\[\sqrt{96}-\sqrt{6}+2\]

Answer 12

So out of those answer choices you have, you know it can't be B and D because they are being added by 10 and not 2, so you know the answer must be A or C... now for the gran finale!!!!! :D

Answer 13

So to simplify a radical you need to find all the smallest numbers that multiply to the number inside:
so for 96 it would be \[\sqrt{2 \times 2 \times 2 \times 2 \times 2 \times 3}\]
Now we are gonna make it like Noah's ark, the radical is the land and the outside is the Boat, we need to make pairs of 2 of the name number <3
So
So now when we bring the pairs to the outside, each pair becomes 1 of that number (so now we have two 2s. and we are gonna multiply them together.
So now \[\sqrt{96}\] is simplified to
\[4\sqrt{6}\]