Question

What is the following quotient? StartFraction 3 StartRoot 8 EndRoot Over 4 StartRoot 6 EndRoot EndFraction.

Answer 1

You can simplify the given expression by taking out those factors who are perfect squares.

The simplified form  of the given expression will be  $\dfrac{\sqrt{3}}{2}$

How to simplify values which are under the root?

If possible, try to defactor what is inside the root.

For example, if 8 is under square root, then you can defactor 8 as made up of 2 times 2 times 2. Since 2 times 2 is perfect square, thus this can come out of the root.

Simply, some more such methods can be used to simplify these type of values.

Using the simplification method on given expression

$\dfrac{3\sqrt{8}}{4\sqrt{6}} = \dfrac{3\sqrt{2 \times 2 \times 2}}{4\sqrt{6}}\\\\ \dfrac{3\sqrt{8}}{4\sqrt{6}} = \dfrac{3 \times 2\sqrt{2}}{4\sqrt{6}}\\ \\ \dfrac{3\sqrt{8}}{4\sqrt{6}} = \dfrac{6\sqrt{2}}{4\sqrt{6}} = \dfrac{\sqrt{6}\sqrt{2}}{4}\\\\ \dfrac{3\sqrt{8}}{4\sqrt{6}} = \dfrac{\sqrt{12}}{4} = \dfrac{\sqrt{4 \times 3}}{4} = \dfrac{\sqrt{3}}{2}$

Thus, after getting simplified, the expression becomes $\dfrac{\sqrt{3}}{2}$

Learn more about quotient here:

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