Question

cos(45 °-30 °)
I know how to set this up using sum and Difference Formula. But multiplying radical fractions make 0 sense to me. can someone explain how the answer is (1+sqrt(3))/(2 sqrt(2))

Answer 1

\[\cos(A-B)=\cos Acos B+sinAsinB\]

Answer 2

put A=45 and B=30

Answer 3

\[(\sqrt{2}/\sqrt{2})(\sqrt{3}/2)+(\sqrt{2}/2)(1/2)= (\sqrt{2+3}/2) + (\sqrt{2}/4)\]

Is this the correct process?

Answer 4

you mean sqrt(2)/2 not sqrt(2)/sqrt(2)

when you multiply fractions, you multiply top*top and bottom * bottom

Answer 5

sorry for the incorrect input of my answers.... Im new to this

Answer 6

\[(\sqrt{2}+\sqrt{3}/2) + (\sqrt{2}/4)\]

Answer 7

If you use the equation editor, it's easier to put in the correct equation.

but you start with
\[ \frac{\sqrt{2}}{2} \cdot \frac{\sqrt{3}}{2} +\frac{\sqrt{2}}{2} \cdot \frac{1}{2} \]

Answer 8

you did the right-hand side fraction multiply correctly: sqrt(2)*1 is sqrt(2) for the top
and 2*2= 4 for the bottom

try again for the left fractions

Answer 9

btw, you can write either
\[ \sqrt{2}\cdot\sqrt{3} \]
or
\[ \sqrt{2\cdot3}= \sqrt{6} \]

Answer 10

so the answer is
\[ \frac{\sqrt{2}}{2} \cdot \frac{\sqrt{3}}{2} +\frac{\sqrt{2}}{2} \cdot \frac{1}{2} = \frac{\sqrt{2}\cdot \sqrt{3} + \sqrt{2}}{4} \]
you could "factor out" a sqrt(2) from each term in the top and write the expression as
\[ \frac{\sqrt{2}(\sqrt{3} + 1)}{4} \]

Though it is generally not done to put a square root in the denominator , you could multiply top and bottom by sqrt(2)
\[ \frac{\sqrt{2}(\sqrt{3} + 1)}{4} \cdot \frac{ \sqrt{2}}{\sqrt{2}}\]

Answer 11

can you finish ?

Answer 12

no Im stuck! haha. I know the answer is : \[(1+\sqrt{3})/(2\sqrt{2})\]

I dont understand how to get this answer

Answer 13

for this
\[ \frac{\sqrt{2}(\sqrt{3} + 1)}{4} \cdot \frac{ \sqrt{2}}{\sqrt{2}} \]
you multiply top times top and bottom times bottom
we can change the order of multiplication so we can write it as
\[ \frac{\sqrt{2}\sqrt{2}(\sqrt{3} + 1)}{4\sqrt{2}} \]

what is sqrt(2)*sqrt(2) ?

Answer 14

you could use a calculator, but you should learn that
sqrt(something)*sqrt(something)= something

where the something inside the square root is the same thing

1??
is your calculator broken ?

Answer 15

\[\sqrt{2}\times \sqrt{2}\]=1.682

Answer 16

sorry I'm having the hardest time with this and it should be easy! thank you for your help

Answer 17

\[ \sqrt{2}\times \sqrt{2} \]

out of curiosity how did you get 1.682 ?

Answer 18

ok you did
\[ \sqrt{2 \sqrt{2}} \]
which is not what you want.

you could type this into the google search window
sqrt(2)*sqrt(2)=

Answer 19

ok it would be 2.

Answer 20

yes, now what do we have for your problem after replacing sqrt(2)*sqrt(2) with 2

Answer 21

when you have time, take a look at
http://www.khanacademy.org/math/arithmetic/exponents-radicals/radical-radicals/v/simplifying-radicals

Answer 22

\[\frac{ 2(\sqrt{3}+1) }{ 4\sqrt{2} }\]

Answer 23

do you know you can simplify by dividing top and bottom by 2
(or multiply top and bottom by 1/2)
what do you get ?

Answer 24

in other words
2/4 is the same as 1/2

Answer 25

\[ \frac{ \sqrt{3} +1}{ 2\sqrt{2} }\]

Answer 26

after dividing by 2 thats what I got

Answer 27

does that look familiar ?

Answer 28

that's the final answer. I just don't feel comfortable doing these problems yet. Hopefully it will click before my test ! Thank you for your help!

Answer 29

I would watch the Khan videos on radicals (and fractions if you need help there)
There are only a few "rules" to learn, and then some practice so it sinks in.

Answer 30

ok, im watching it now! forgot about this website, very helpful