How do you simplify #2sqrt6-sqrt24#?

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Answer 1 · 2016-08-04T10:30:11

#0#

Write the numbers as the product of prime factors to see what we are working with..

#2sqrt6 - sqrt24 #
=#2sqrt(2xx3) - sqrt((2xx2)xx2xx3)#

=#2sqrt6 - 2sqrt6#

=#0#

Answer 2 · 2016-08-04T10:35:19

#2sqrt(6)-sqrt(24)=0#

Look for common factors

#color(blue)("Method 1 - taking values out of the root")#
Consider 12: this can be split into #2^2xx6#

Write as: #2sqrt(6)-sqrt(2^2xx6)#

#color(green)(2sqrt(6)-2sqrt(6)=0)#

'~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~

#color(blue)("Method 2 - taking values into the root")#

Consider #2sqrt(6)#
We know that #2=sqrt(4)=sqrt(2^2)#

So we have a way of taking the 2 into the square root without changing the overall value

#color(brown)(2sqrt(6)-sqrt(24)color(blue)(" "->" "sqrt(2^2xx6)-sqrt(24)#

But #2^2xx6=4xx6=24# giving:

#color(green)(sqrt(24)-sqrt(24)=0)#