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

1 Answer
Eivind K.
Nov 8, 2015
  • 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)#

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