How do you evaluate 2\sqrt { 24} - \sqrt { 3} - 2\sqrt { 27}?

2 Answers
May 4, 2017

4sqrt6-7sqrt3

Explanation:

expand all numbers:

2sqrt24= sqrt4 * sqrt24

=sqrt(4*24)

=sqrt96

2sqrt27 = sqrt4 * sqrt27

=sqrt(4*27)

=sqrt108

2sqrt24 - sqrt3 - 2sqrt27 = sqrt96 - sqrt3 - sqrt108

find all numbers as multiples of sqrt3:

sqrt96 = sqrt3 * sqrt32 = sqrt3 * 2sqrt8 or (sqrt32)(sqrt3)

sqrt108 = sqrt3 * sqrt36 = 6sqrt3

2sqrt24 - sqrt3 - 2sqrt27 = (sqrt32)(sqrt3) - sqrt3 - 6sqrt3

=(sqrt32-1-6)(sqrt3) = (sqrt32-7)(sqrt3) or (4sqrt2-7)(sqrt3)

multiplied out, this is:

4sqrt6-7sqrt3

May 13, 2017

Shorter way to get 4sqrt(6)-7sqrt(3)

Explanation:

Break down the values inside the square root into their smallest components:

2sqrt(2xx2xx2xx3) -sqrt(3)-2sqrt(3xx3xx3)

If there are two of the same numbers, then you can take them out of the square root. For example, sqrt(2xx2) can be taken out as 2

2(2)sqrt(2xx3)-sqrt(3)-2(3)sqrt(3)

Clean up the problem by multiplying everything together:

4sqrt(6)-sqrt(3)-6sqrt(3)

The -sqrt(3) and -6sqrt(3) can be combined by adding the coefficients together:

-1+(-6)=-7

So we have:

4sqrt(6)-7sqrt(3)