Question

What is the following quotient

Answer 1

√(3)/2

Explanation:

To find the quotient, rationalize the denominator by multiplying both the numerator and denominator by √(6)

3√(8)*√(6) = 3√(48)

4√(6)*√(6) 24

Next, simplify the top radical

12√(3) = √(3)/2, This is the answer, it cannot be simplified any further.

24

Answer 2

For this case we must find the quotient of the following expression:

`\frac {3 \sqrt {8}} {4 \sqrt {6}} =`

We combine
`\sqrt {6}` and
`\sqrt {8}` into a single radical:

`\frac {3 \sqrt {\frac {8} {6}}} {4} =\\\frac {3 \sqrt {\frac {4} {3}}} {4} =\\\frac {3 \frac {\sqrt {4}} {\sqrt {3}}} {4} =\\\frac {3 \frac {2} {\sqrt {3}} * \frac {\sqrt {3}} {\sqrt {3}}} {4} =`

`\frac {3 * \frac {2 \sqrt {3}} {3}} {4} =\\\frac {\frac {6 \sqrt {3}} {3}} {4} =\\\frac {6 \sqrt {3}} {12} =\\\frac {\sqrt {3}} {2}`

Answer:

`\frac {\sqrt {3}} {2}`