Question #1eeb2

1 Answer
Mar 1, 2017

Answer:

#2sqrt(3)#

Explanation:

In this format the brackets do not do anything so disregard them.

#15/sqrt(3)-sqrt(27)#

Mathematicians do not like roots in the denominator so lets 'get rid' of it. Multiply by 1 and you do not change a value. However, 1 comes in many forms so you can change the way something looks without changing its intrinsic value.

#color(green)([15/sqrt(3)color(red)(xx1)]-sqrt(27)#

#color(green)([15/sqrt(3)color(red)(xxsqrt(3)/sqrt(3))]-sqrt(27)#

#color(green)([(15sqrt(3))/3]-sqrt(27))#

But #sqrt(27) = sqrt(3xx9)=sqrt(3xx3^2)=3sqrt(3)#

#(15sqrt(3))/3-3sqrt(3)#

Factor out the #sqrt(3)#

#sqrt(3)xx[15/3-3]#

#sqrt(3)xx6/3#

#2sqrt(3)#