How do you simplify 2sqrt6-sqrt24?

2 Answers
Aug 4, 2016

0

Explanation:

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

Aug 4, 2016

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

Explanation:

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)