Question

could someone help me figure out how to solve this problem step by step? it is Algebra 2

Answer 1

that is the problem.

Answer 2

i know the answer is -3/2+1/2 sqrt 5 just need to know how to get to it

Answer 3

you need to multiply top and bottom by the conjugate

\[\sqrt{2}- \sqrt{10}\]

Answer 4

what is the conjugate?

Answer 5

bottom line is

\[\sqrt{2} + \sqrt{10}\]

so the conjugate is

\[\sqrt{2} -\sqrt{10}\]

Answer 6

so do i multiply \[\sqrt{2}*\sqrt{2}\]

Answer 7

or do i find the square root first

Answer 8

First multiply the top line by the conjugate

\[(\sqrt{2} -\sqrt{10})(\sqrt{2}-\sqrt{10})\]

Answer 9

then multiply the bottom line by the conjugate

\[(\sqrt{2}+\sqrt{10})(\sqrt{2}-\sqrt{10})\]

Answer 10

so would it be \[\sqrt{4}+\sqrt{100}\] and \[\sqrt{4}-\sqrt{100}\]

Answer 11

help?

Answer 12

no

Answer 13

what do i do??

Answer 14

\[\frac{\sqrt2-\sqrt{10}}{\sqrt2+\sqrt{10}}\times \frac{\sqrt2-\sqrt{10}}{\sqrt2-\sqrt{10}}\]is a start i.e. multiply by the conjugate

Answer 15

the denominator is \(2-10=-8\)

Answer 16

the numerator is whatever you get when you multiply out doing the usual four multiplications

Answer 17

you know how to multiply out?

Answer 18

no

Answer 19

\[(a-b)(a-b)=a^2-2ab+b^2\]

Answer 20

im confused.. i do not understand this at all

Answer 21

want to start over?

Answer 22

yes please

Answer 23

@satellite73

Answer 24

help?

Answer 25

\[\sqrt{2}-\sqrt{5}+\sqrt{10}\]
thats the answer

Answer 26

Are you still there?

Answer 27

yes