Question

What is the following quotient? 3 sqrt 8 / 4 sqrt 6

A. 12 sqrt 2-6 sqrt 3 / 5
B.3 sqrt 6 -4 sqrt 3 / 24
C.sqrt 3/12
D.sqrt 3/2

Answer 1

The correct option is D)
`(√(3))/(2)`

Explanation:

We need to find out the quotient of
`(3√(8))/(4√(6))`

`=(3√(8))/(4√(6))`

Rewrite the above expression;

`=(3*2 √(2))/(4√(6))`

`=(6√(2))/(4√(6))`

Cancel out the common term from numerator and denominator,

`=(3√(2))/(2√(6))`

`=(3√(2))/(2√(2)* √(3))`

`=(3)/(2√(3))`

Multiply numerator and denominator with
`√(3)`

`=(3√(3))/(2√(3)√(3))`

`=(3√(3))/(2* 3)`

`=(3√(3))/(6)`

`=(√(3))/(2)`

Therefore, the correct option is D)
`(√(3))/(2)`

Answer 2

For this case we have the following expression:
3sqrt (8) / 4sqrt (6)
Rewriting we have:
3sqrt (2 * 4) / 4sqrt (6)
3 * 2sqrt (2) / 4sqrt (6)
6sqrt (2) / 4sqrt (6)
3sqrt (2) / 2sqrt (6)
3sqrt (2) / (2sqrt (2) sqrt (3))
3 / (2sqrt (3))
3sqrt (3) / (3 * 2)
sqrt (3) / (2)
Answer:
the following quotient is:
D.sqrt 3/2