Question

@AZ more math

Answer 1

hmm

\(\dfrac{1}{\sqrt{18}} \times \dfrac{\sqrt{18}}{\sqrt{18}} = \dfrac{\sqrt{18}}{18}\)


So this is the question

\(\dfrac{1}{\sqrt{2} + \dfrac{1}{\sqrt{8} + \sqrt{200} +\dfrac{1}{\sqrt{18}}}}\)

so we have to solve the innermost fractions and work our way out

Answer 2

ok so how do u simplfy
1/(sqrt(8)+sqrt(200)+sqrt(18)/18)

Answer 3

\(\dfrac{1}{\sqrt{2} + \dfrac{1}{\sqrt{8} + \sqrt{200} +\dfrac{\sqrt{18}}{18}}}\)

Now,

\(\sqrt{8}\) and \(\sqrt{200}\)

can you write it down in the most simplest form?

hint:
8 = 2^2 * 2
200 = 10^2 * 2

Answer 4

the current goal is to write that entire line as a fraction

Answer 5

ok so
2sqrt(2)+10sqrt(2)
so
1/(12sqrt(2)+sqrt(18)/18)

Answer 6

\(\sqrt{8} + \sqrt{200} +\dfrac{\sqrt{18}}{18} = ??\)

Answer 7

\( 2\sqrt{2} + 10\sqrt{2} + \dfrac{\sqrt{18}}{18} \)

\( = 12\sqrt{2} + \dfrac{\sqrt{18}}{18} \)

and can you simplify sqrt(18) first?

Answer 8

18 = 9 * 2 = 3^2 * 2

Answer 9

sqrt(18)=3sqrt(2)

Answer 10

\( = 12\sqrt{2} + \dfrac{\sqrt{18}}{18} \)

\(= 12\sqrt{2} + \dfrac{3\sqrt{2}}{18}\)

\( =12\sqrt{2} + \dfrac{\sqrt{2}}{6}\)

now can you make it have the same denominator?

Answer 11

um (72sqrt(2)+sqrt(2))/6

Answer 12

then (73sqrt(6)/6)

Answer 13

Yes and 72sqrt(2) + sqrt(2) is 73sqrt(2)

So now we started with

\(\dfrac{1}{\sqrt{2} + \dfrac{1}{\sqrt{8} + \sqrt{200} +\dfrac{1}{\sqrt{18}}}}\)

And now we have

\(\dfrac{1}{\sqrt{2} + \dfrac{1}{\dfrac{73\sqrt{2}}{6}}}\)

Answer 14

so you would have to find
sqrt(2)+6/73sqrt(2)

Answer 15

Now let's just flip the fraction

we have

\(\dfrac{1}{\dfrac{73\sqrt{2}}{6}}=\)

and yup yup yup!

Answer 16

\(\dfrac{1}{\sqrt{2} + \dfrac{6}{73\sqrt{2}}}\)

So just focus on simplifying the denominator right now

Answer 17

If you multiply the first fraction by sqrt(2) / sqrt(2)

then you'll get the same denominator and then can add the fractions

Answer 18

wait oops

I mean, we'd have to multiply by 73sqrt(2)

Answer 19

We need to multiply it by that so that way we'd have the same denominator to add the fractions

Answer 20

ok then
is it
3sqrt(2)/73?

Answer 21

Hmm no


\(\dfrac{1}{\dfrac{73\sqrt{2}\times \sqrt{2}}{73\sqrt{2}} + \dfrac{6}{73\sqrt{2}}}\)


\( 73\sqrt{2}\times \sqrt{2} = 73 \times 2 = ??\)

Answer 22

oh wait i thought you ment the other fraction
ok so its
146

Answer 23

152/73sqrt(2)
then its
73sqrt(2)/152

Answer 24

There you go! and I think that's all you can simplify it to

Answer 25

ok thank you

Answer 26

You're welcome :)