Question

Simplify: 5 sqrt 3 (2 sqrt 3 + 6 sqrt 19)
30 + 30 sqrt 57
90 + 30 sqrt 57
10 sqrt 3 + 30 sqrt 19
10 sqrt 3 + 30 sqrt 57

Answer 1

same idea: distribute then combine sqrt's

Answer 2

im not sure how i would but it in distubutive property

Answer 3

put

Answer 4

5 srqt 3 (2 sqrt3 sqrt 3 + 6 sqrt 3 sqrt 19)??

Answer 5

in letters:
A * (B+C) = A*B + A*C

take the "stuff" in front (in this case 3 sqrt3 ) and multiply it times each thing inside

Answer 6

5 sqrt 3 (2 sqrt 3 + 6 sqrt 19)

you have two terms inside the parens: 2 sqrt3 and 6 sqrt19
you multiply each term by 5 sqrt3
for the first term just write it like this
5*sqrt3 * 2 * sqrt3 ( I put in * to show the multiplication, but in algebra you normally don't show the multiplication sign, and just know it is there.)

however, put the numbers first (when you multiply you can switch the order)
5*2 * sqrt3 * sqrt3

you know what 5*2 is , right ?
do you know what sqrt3 * sqrt3 is ?

and do the same thing for the 2nd term: 6 sqrt19

Answer 7

ok so 10 sqrt 6
and 5 * sqrt 3 * 6 * sqrt 19
giving me 5 * 6
and sqrt 3 * sqrt 19
then giving me 30 sqrt 57
Answer = 10 sqrt 6 + 30 sqrt 57

Answer 8

giving me 5 * 6
and sqrt 3 * sqrt 19
then giving me 30 sqrt 57
that part is correct.

do the first part again
5*2 * sqrt3 * sqrt3

Answer 9

5*2 = 10
sqrt 3 * sqrt 3 = sqrt 9
10 sqrt 9

Answer 10

yes. but what is the square root of 9 ?

Answer 11

3

Answer 12

yes so 10*sqrt(9) is 10*3 or 30

Answer 13

ok

Answer 14

so right now im looking at D for my answer

Answer 15

what is the first term?
(5*2 * sqrt3 * sqrt3) + (5 * sqrt 3 * 6 * sqrt 19)

Answer 16

the first term is 10 sqrt 9
simplified its 10 sqrt 3

Answer 17

next term is 30 sqrt 57

Answer 18

the first term is 10 sqrt 9
simplified its 10 sqrt 3 <-- no. sqrt(9) is 3

square root of 9 is 3 because 3*3=9

Answer 19

ok

Answer 20

so if you see sqrt(3*3) you know that is 3

Answer 21

ok

Answer 22

so, the answer for this question is
10 sqrt 9
simplified its 10 *3 =30
for the first term.

Answer 23

ok

Answer 24

can you get the answer ?

Answer 25

A

Answer 26

yes,

also I noticed a typo in my rules:
sqrt(x) * sqrt(x) = x is the rule

or sqrt( x*x) = x
or
sqrt(x^2) = x <-- (it is x, not 2 like I had)
those are 3 different ways of saying the same thing.

try to remember this rule.

Answer 27

ok thanks i'll post the last question if ur ready

Answer 28

ok