Basic Algebra. Simplify Expressions?

Question

I'm having trouble finding formulas in my book, and does not show examples. All I'm asking for are the formulas, not the answers. but if you want to give the answer, i am not going to argue.
Thanks


Simplify the expression

1. 6√2 divided by √3

a. 6√3
b. 2√6 / 3
c. 2√6
d. 2√3

2. simplify 2√20 - 3√7 - 2√5 + 4√63


3. simplify √96 divided by √8

a. 4√3 over √2
b. √2 over 4
c. 2√3
d. 1 over 2√3

Answer 1

Basic Algebra. Simplify Expressions?
I'm having trouble finding formulas in my book, and does not show examples. All I'm asking for are the formulas, not the answers. but if you want to give the answer, i am not going to argue.
Thanks


Simplify the expression

1. 6√2 divided by √3

a. 6√3
b. 2√6 / 3
c. 2√6
d. 2√3
none of the above.it will be rt6

2. simplify 2√20 - 3√7 - 2√5 + 4√63
4rt5-3rt7-2rt5+9rt7
=2rt5+6rt7

3. simplify √96 divided by √8

c. 2√3

Answer 2

There are no exact formulas to solve these, just techniques you can learn to use.

1) you can include the 6 under the square root... the square root of 36 is 6, so another way of writing 6√2 is: √36*√2 = √72

then, just divide by √3:
= √72/√3
= √(72/3)
= √24
= √(6*4)
= 2√6

2) simplify by finding factors in the square roots that can be taken out:
= 2√(5*4) - 3√7 - 2√5 + 4√(7*9)
= 2*2√5 - 3√7 - 2√5 + 4*3√7
= 4√5 - 3√7 - 2√5 + 12√7
= (4-2)√5 + (12-3)√7
= 2√5 + 9√7

3)
= √96/√8
= √(16*6) / √(4*2)
= √16*√6 / √4*√2
= 4√6 / 2√2
= 2√6 / √2

Answer 3

6√2 / √3 =

6√2√3 / √3√3 =

6√6 / √9 =

6√6 / 3 =

2 √6

- - - - - - - -

2√20 - 3√7 - 2√5 + 4√63 =

2 √4√5 - 3√7 - 2√5 + 4 √9√7 =

2 x 2 √5 - 3√7 - 2√5 + 4 x 3 √7 =

4√5 - 3√7 - 2√5 + 12 √7 =

4√5 - 2√5 + 12√7 - 3√7 =

4 - 2√5 + 12 - 3√7 =

2√5 + 9√7

- - - - - - - -

√93 / √8 =

√8√12 / √8 =

√12 =

√4√3 =

2 √3

- - - - - - - - -s-

Answer 4

Question 1
6.√2 / √3 = 6.√2.√3 / 3 = 2.√6

Question 2
2√(4 x 5) - 3√7 - 2√5 + 4√(7 x 9)
4√5 - 3√7 - 2√5 + 12√7
2√5 + 9√7

Question 3
√96 / √8 = √8.√12 / √8 = √12 = 2√3
ANSWER c)

Answer 5

1) c. 2√6

2) 2√20 - 3√7 - 2√5 + 4√63
4√5-2√5-3√7+12√7
= 2√5+9√7

3) c. 2√3

Answer 6

Q1
6√2 divided by √3
multiply and divide by √3
u'll get 2√6

Q2
2√20 - 3√7 - 2√5 + 4√63
4√5 - 3√7 - 2√5 + 12√7
2√5 + 9√7

Q3
√96 divided by √8
multiply n divide by √8
the answer is 2√3

Answer 7

6*sqrt 2 / sqrt 3

You can't have a sqrt in the denominator, so multiply the top and bottom by sqrt 3

6 * sqrt 2 * sqrt 3 / (sqrt 3)^2
= 6 * sqrt 6 / 3
= 2 * sqrt 6

--------
2*sqrt 20 =
2* sqrt (4 * 5) =
2*sqrt 4 * sqrt 5 =
2*2*sqrt 5 =
4*sqrt 5

4* sqrt 63 =
4 * sqrt (9 * 7) =
4 * sqrt 9 * sqrt 7 =
4 * 3 * sqrt 7 =
12 * sqrt 7

Now you have:
4*sqrt 5 - 3*sqrt 7 - 2*sqrt 5 + 12*sqrt 7 =
(4*sqrt 5 - 2*sqrt 5) + (12*sqrt 7 - 3*sqrt 7) =
2*sqrt 5 + 9*sqrt 7

(that's as far as you can simplify)
------------------------
sqrt 96 / sqrt 8 =
sqrt (96/8) =
sqrt 12 =
sqrt (4*3) =
sqrt 4 * sqrt 3 =
2 * sqrt 3

Answer 8

1. 6 = 2 * 3 = rt(2) * rt(2) * rt(3) * rt(3)
so 6 * rt(2) / rt(3) = rt(2)*rt(2)*rt(2)*rt(3) = 2 rt(6)
--> answer c

2. rt(63) = rt(9*7) = 3 rt(7)
rt(20) = rt(4*5) = 2 rt(5)
--> answer 2 rt(5) + 9 rt(7)

3. rt(96) = rt(16*6) = 4 rt(6) = 4 rt(2) * rt(3)
rt(8) = rt(4*2) = 2 * rt(2)

rt(96) / rt(8) = 2 rt(3) --> answer c

Answer 9

1) answer c 2sqrt6

2) 28.284 or 4sqrt50

3) answer c 2sqrt3