Question

√108 - 3√50 + 5√12 + 4√18
I'm kind of confused on how to simplify..

Answer 1

Notice how

\[\Large \sqrt{108} = \sqrt{36*3}\]

\[\Large \sqrt{108} = \sqrt{36}*\sqrt{3}\]

\[\Large \sqrt{108} = 6\sqrt{3}\]

Answer 2

I'm factoring the number into two numbers where one number is a perfect square

Answer 3

Then I'm breaking up the root and simplifying

Answer 4

Use this idea to simplify the other roots

Answer 5

Would the second one be,

Answer 6

3√(25*2)=3√25*√2=3*5√2

Answer 7

which becomes \[\Large -15\sqrt{2}\]

Answer 8

Why -15?

Answer 9

because it was -3 instead of +3

Answer 10

in front of the square root of 50

Answer 11

What about the last one.. 4√18

Answer 12

hold on, what did you get for 5√12

Answer 13

did you manage to simplify that at all?

Answer 14

For 5√12, I got 10√3 ?

Answer 15

good

Answer 16

for 4√18

factor 18 into 9*2, then simplify

Answer 17

Thank you!

Answer 18

you're welcome, tell me what your final answer is

Answer 19

6√3 - 5√2 + 10√3 + 12√2

Answer 20

i mean, -15√2

Answer 21

√108 - 3√50 + 5√12 + 4√18

should be

6√3 - 15√2 + 10√3 + 12√2


Notice it's -15√2 and not -5√2

Answer 22

Now combine like terms

Answer 23

16√3 - 3√2

Answer 24

good, you nailed it

Answer 25

[:

Answer 26

Verification:

http://www.wolframalpha.com/input/?i=%E2%88%9A108+-+3%E2%88%9A50+%2B+5%E2%88%9A12+%2B+4%E2%88%9A18+%3D+16%E2%88%9A3+-+3%E2%88%9A2+

Answer 27

Another way to verify is to type in

(√108 - 3√50 + 5√12 + 4√18) - (16√3 - 3√2)

into your calculator

If you get the result of 0 (or very very close to it), then you have verified the answer