Question

How do find the quotient of `(-4sqrt3 )/( 3sqrt2)`?

Answer 1

• Rewrite the square roots to exponents
• A little bit of algebra
  .. and you will get the answer `-sqrt(8)/sqrt(3)`

Explanation:

Sometimes square roots can be painful to work with, so we have some rules that we can use to rewrite them. One of them is:
`sqrt(a) = a^(1/2)`
And this is the one we will use for this problem.

We also need to know how to deal with eventual negative exponents. Let's have an example:
`a^(-n) = 1/(a^n)`
In this problem, we will use this rule the other way around as well. So let's start!

To make it easier for us, we can split up the expression into parts; one for the base of 2, and one of the base of 3:

`(-4sqrt(3))/(3sqrt(2)) = (-4)/sqrt(2) * sqrt(3)/3`

Let's tweek on the expression so we can see the exponents

`-2^2/2^(1/2) * 3^(1/2)/3`

Now, let's move the factors to the same place, using the formula `a^(-n) = 1/(a^n)`:

`(-2^2 * 2^(-1/2))/1 * 1/(3^1*3^(-1/2))`
`= -2^(2/2-1/2)/1 * 1/(3^(2/2 - 1/2)`
`= -2^(3/2)/1 * 1/3^(1/2)`
`= -sqrt(2^3)/sqrt(3)`
`= -sqrt(8)/sqrt(3)`