How do you rationalize the denominator and simplify #sqrt(2/3)#?

Question

988 views around the world

You can reuse this answer
Creative Commons License

Answer 1 · 2016-05-09T12:45:30

#sqrt(6)/3#

It is mathematically frowned up to have a root in the denominator. So it is better to 'get rid' of it if you can.

This is done using the following 'trick'!

If you multiply a value by 1 you do not change its 'worth'

#2xx1=2# and so on

The value 1 can be written in many forms: #4-3; 0+2; 2/2 ; sqrt(3)/sqrt(3)#
'~~~~~~~~~~~~~~~~~~~~~~~~~
Given#" "sqrt(2/3)#

Write as:#" "sqrt(2)/(sqrt(3))#

Multiply by 1 but in the form of #1=sqrt(3)/sqrt(3)# giving

#" "sqrt(2)/(sqrt(3))xxsqrt(3)/(sqrt(3))#

#" "(sqrt(2)xxsqrt(3))/(sqrt(3))^2#

#sqrt(2xx3)/3 = sqrt(6)/3#