Question

Help with subtracting radicals?

Answer 1

54 and 24 both have a factor of 6 in them

Answer 2

Okay so 3sqrt( 9 * 6) - 4sqrt(4 * 6)

Answer 3

yes. does that help? can we split square roots ??

Answer 4

Well yes but I don't know how to continue

Answer 5

split square roots?

Answer 6

that way we could cancel away +sqrt(6) and -sqrt(6)

Answer 7

maybe

Answer 8

wait \[3 \times \sqrt{9} \times \sqrt{6} - 4 \times \sqrt{4} \times \sqrt{6}\]

Answer 9

is that splitting?

Answer 10

yes. I'm not really sure how to simplify fractions though
just saw the 6 factor and thought it may be part..

Answer 11

how to simplify square roots*

Answer 12

Ohh, well thanks anyway!

Answer 13

what is the square root of 9?

Answer 14

3

Answer 15

what is the square root of 4

Answer 16

2

Answer 17

so

\[3 \times \sqrt{9} \times \sqrt{6} - 4 \times \sqrt{4} \times \sqrt{6}\]

turns into

\[3 \times 3 \times \sqrt{6} - 4 \times 2 \times \sqrt{6}\]

and that becomes

\[9\sqrt{6} - 8\sqrt{6}\]


I'll let you finish up

Answer 18

is the answer 1?

Answer 19

1 what

Answer 20

if it helps, think of \(\large \sqrt{6}\) as x

so if you do that, then

\[9\sqrt{6} - 8\sqrt{6}\]

turns into

\[9x - 8x\]

after you make the replacements

Answer 21

1sqrt6? If that's right why didn't the sqrts cancel out?

Answer 22

That would equal x

Answer 23

because it is subtraction and not division :)

Answer 24

like with the xes

Answer 25

Ohh

Answer 26

if x = sqrt(6)

then

9*sqrt(6) - 8*sqrt(6)

9x - 8x

(9-8)x

(1)x

1*x

1*sqrt(6)

sqrt(6)


So that shows us how


\[\large 9\sqrt{6} - 8\sqrt{6} = \sqrt{6}\]

Answer 27

Ohh okay that makes sense...would it still have been acceptable if I had left it as 1sqrt6? or does that depend on the teacher?

Answer 28

\(\large 1\sqrt{6}\) is the same as \(\large \sqrt{6}\)

so either one is fine

Answer 29

the second is more simplified in my opinion

Answer 30

Gotcha c: Thanks Jim and Essential! ^_^

Answer 31

you're welcome