Question

Assuming x > 0, which of these expressions is equivalent to 11 sqrt(245x^3) + 9 sqrt(45x^3) ?

Answer 1

@jim_thompson5910

Answer 2

hmm I'm assuming there are answer choices? if not, then just try to simplify 11 sqrt(245x^3) + 9 sqrt(45x^3) as much as possible

Answer 3

what comes after 104 sqrt(5) sqrt(x^3)

Answer 4

how are you getting that

Answer 5

idk how to do the sqrt thing so im trying my best lol

Answer 6

ok forget what i said how do i simplify that ?

Answer 7

can you factor 245 into two numbers where one factor is a perfect square?

Answer 8

yes? or no?

Answer 9

i can try..

Answer 10

alright tell me what you get

Answer 11

5 * 49 ?

Answer 12

good

Answer 13

so

\[\large \sqrt{245} = \sqrt{5*49}\]

\[\large \sqrt{245} = \sqrt{49*5}\]

\[\large \sqrt{245} = \sqrt{49}*\sqrt{5}\]

\[\large \sqrt{245} = 7*\sqrt{5}\]

see how I'm getting this?

Answer 14

yes i got it

Answer 15

ok so this means

\[\large \sqrt{245x^3} = \sqrt{5*49x^2*x}\]

\[\large \sqrt{245x^3} = \sqrt{49x^2*5x}\]

\[\large \sqrt{245x^3} = \sqrt{49x^2}*\sqrt{5x}\]

\[\large \sqrt{245x^3} = 7x*\sqrt{5x}\]

Answer 16

Then we can cay

\[\large 11\sqrt{245x^3} = 11\sqrt{5*49x^2*x}\]

\[\large 11\sqrt{245x^3} = 11\sqrt{49x^2*5x}\]

\[\large 11\sqrt{245x^3} = 11\sqrt{49x^2}*\sqrt{5x}\]

\[\large 11\sqrt{245x^3} = 11*7x*\sqrt{5x}\]

\[\large 11\sqrt{245x^3} = 77x*\sqrt{5x}\]

Answer 17

Use these ideas to simplify \(\large 9\sqrt{45x^3}\)

Answer 18

i have to find what times what = 45 right ?

Answer 19

yep, factor it and make sure one factor is a perfect square

Answer 20

my OS is acting weird sorry....... can it be 9 * 5 ?

Answer 21

@jim_thompson5910

Answer 22

yep, 45 = 9*5

use this to get

\[\large 9\sqrt{45x^3} = 9\sqrt{9*5x^2*x}\]


\[\large 9\sqrt{45x^3} = 9\sqrt{9x^2*5x}\]


\[\large 9\sqrt{45x^3} = 9\sqrt{9x^2}*\sqrt{5x}\]


\[\large 9\sqrt{45x^3} = 9*3x*\sqrt{5x}\]


\[\large 9\sqrt{45x^3} = 27x*\sqrt{5x}\]

Answer 23

@jim_thompson5910 what happens after that ?

Answer 24

\[\large 11\sqrt{245x^3} + 9\sqrt{45x^3} \]

turns into

\[\large 77x*\sqrt{5x} + 27x*\sqrt{5x} \]

Answer 25

what's next

Answer 26

ummmmmmm

Answer 27

add 77 + 27 ?

Answer 28

good

Answer 29

to get ?

Answer 30

104x

Answer 31

then just add the sort(5x) .... so the answer would be 104x sqrt(5x)

Answer 32

so

\[\large 77x*\sqrt{5x} + 27x*\sqrt{5x} \]

turns into

\[\large 104x*\sqrt{5x} \]

yep you got it

Answer 33

thank you :)

Answer 34

sure thing