Question

Assuming x > 0, which of these expressions is equivalent to 11 times the square root of 245 x to the third plus 9 times the square root of 45 x to the third? ?

Answer 1

heya

Answer 2

Hey :)

Answer 3

...which of which expressions dude, is there more to the q...?

Answer 4

Umm...let me see..

5 x times the square root of 104 x

20 times the square root of 290 x to the sixth

20 x times the square root of 290 x

104 x times the square root of 5 x

Answer 5

k
so use BODMAS rules to kinda guess the order of operations here:

i think the question looks something like:

Answer 6

11 times the square root of 245 x to the third plus 9 times the square root of 45 x to the third? ?

\[11 \times \sqrt{245x ^{3}} + \sqrt{45x ^{3}}\]

Answer 7

but it may be ... (245x)^3 and (45x)^3 ... which changes everything

but lets assume the first guess is correct and see how we go

Answer 8

Here ill type it up. :)

Answer 9

cool

Answer 10

\[11\sqrt{245^3} + 9\sqrt{45^3}\] There ya go^^

Answer 11

ah, nice, i missed the 9, cheers man

Answer 12

lol your helping me a ton already thanks ^-^

Answer 13

so, starting at the back, the factors of 45 are:
9 and 5
so sqrt 45 = (sqrt 5) times (sqrt 9)
= (sqrt 5) times (3)
\[=3 \sqrt{5}\]

Answer 14

now sqrt is the same as (to the power of half)

so \[\sqrt{x ^{3}} = (x ^{3})^{0.5} = (x ^{3})^{1/2} = x ^{(3\times(1/2)}\]

\[= x ^{3/2}\]

Answer 15

so expanding that out
youve got
9 * 3 * x^(3/2) * sqrt 5
= 27 * sqrt 5 * x^(3/2)

Answer 16

You may have just lost me lol :P

Answer 17

bear with me, it'll come together and make sense at the end, promise

Answer 18

lol k :D

Answer 19

now the start
factors of 245
= 5 and 49 (5*49=245)
and 49 = 7 *7 = 7^2

so sqrt of 245 = sqrt 49 times sqrt 5
= 7 times sqrt 5

\[=7\sqrt{5}\]

Answer 20

so 11 times sqrt (245x^3)
= 11 * 7 * sqrt 5 * x^(3/2)

Answer 21

\[x ^{(3/2)} = x \times \sqrt{x}\]

Answer 22

so bring it all together now:

Answer 23

20080√5x^3/2??

Answer 24

11*7 = 77
so 77x * sqrt (5x)

plus

3*9 = 27
so 27x *sqrt (5x)

so final answer should be:
77x * sqrt (5x) + 27x *sqrt (5x)

Answer 25

That ones not up there on the list :'(

Answer 26

if you add the like terms tho
it becomes 104x * sqrt (5x)

Answer 27

you can add the 27 and the 77 together as they are both to the same x value

Answer 28

\[104x \times \sqrt (5x) \]
is one of your answers tho... ;D

Answer 29

Ohhh I see NOW!!!

Answer 30

sweet!
all good, need any clarification on any of the steps dude...?

Answer 31

Nah bro I got it when I look back at it now! :)

Answer 32

noice, slaters then!