Question

When expressed as a single term, what number is the numerical coefficient of the sqrt of 3? (Problem in comments)

Answer 1

\[\sqrt{75}-\frac{ 4 }{ 2\sqrt{3} }\]

Answer 2

@DanJS

Answer 3

@Nnesha

Answer 4

hi

Answer 5

yo.

Answer 6

i should rationalize this right?

Answer 7

what is the prob?

Answer 8

multiply square root of 75 by 2 sq rt of 3?

Answer 9

its up there ^^

Answer 10

\[\frac{ 2\sqrt{3} }{ 2\sqrt{3} } * [\frac{ \sqrt{75} }{ 1 } - \frac{ 4 }{ 2\sqrt{3} }]\]

Answer 11

multiply the whole thing by 1, or 2 root 3 over 2 root 3

Answer 12

just for radical 75 or 4/ 2 radical 3 as well?

Answer 13

distribute it to both of the terms

Answer 14

if i do just to one, the value becomes uneven?

Answer 15

it wont change the value, you are basically multiplying by 1

Answer 16

no, it just will be messier, i think you want to simplify it

Answer 17

then can i do just to radical 75?

Answer 18

you can do it to any of the terms you want, it is just 1, multiplying by 1,
but
if you do it to the root 75 term too, it will simplify to get rid of the root...

Answer 19

yeah that's what i did. i multipled radical 75/1 but 2 radical 3

Answer 20

which equates to 30?

Answer 21

You want to be able to put them over a common denominator, then you can rationalize the denominator

Answer 22

sq rt 225=15 times 2=30

Answer 23

yep, 30 over 2root 3

Answer 24

then i subtracted the 4

Answer 25

26/2 sq rt 3

Answer 26

yeah, now you can rationalize the denominator

Answer 27

i have to rationalize again?

Answer 28

\[\frac{ 26 }{ 2\sqrt{3} } = \frac{ 13 }{ \sqrt{3} } \]

Answer 29

yeah, you just put them over a common denominator in the first step, so you could subtract the two, now you can rationalize the denominator

Answer 30

13root3 over 3

Answer 31

\[\frac{ 13 }{ \sqrt{3} }*\frac{ \sqrt{3} }{ \sqrt{3} } = \frac{ 13\sqrt{3} }{ 3 }\]

Answer 32

what i did wrong was i thought

\[\frac{ 26 }{ 2\sqrt{3} }=13\sqrt{3}\]

Answer 33

it said to express it as a single term, so you had to put them both over the common denominator, then rationalize the root in the denominator

Answer 34

yeah forgot that root 3 times root 3, leaves a 3 in the bottom

Answer 35

you have more ?

Answer 36

not right now, but can you tell me the rule in which my 26/2 sq rt 3 does NOT equal
13 sq root 3

Answer 37

ok

Answer 38

remember that the square root is the same as 'to the 1/2 power right?

Answer 39

yes.

Answer 40

26/2 = 13, so you see it is 13 over root 3 right?

Answer 41

i first thought it was 13 times root 3

Answer 42

\[\frac{ 26 }{ 2 \sqrt{3}} = \frac{ 13 }{ \sqrt{3} }\]

Answer 43

just divided by 2, both top and bottom

Answer 44

ooh. golden words right there, thanks.

Answer 45

now multiply like this , it is a ratio of 1
\[\frac{ 13 }{ \sqrt{3} }*\frac{ \sqrt{3} }{ \sqrt{3} } = \frac{ 13\sqrt{3} }{ \sqrt{3}\sqrt{3} }\]

Answer 46

you get that part?

Answer 47

Yeah, i get that part, the co efficient is 13/3

Answer 48

\[\sqrt{3}\sqrt{3} = 3^{1/2}*3^{1/2} = 3^{1/2 + 1/2} = 3^{1} = 3\]

Answer 49

when you square a square root, you are left with the quantity inside the root

Answer 50

so the final answer is
\[\frac{ 13\sqrt{3} }{ 3 }~~~~or ~~~~\frac{ 13 }{ 3 }*\sqrt{3}\]

Answer 51

coefficient on root 3, 13/3

Answer 52

u understand all of it now?

1) put over common denominator
2) rationalize the denominator
3) simplify

Answer 53

yup. thanks.