# Simplify: 2√27 + 5√8 - 3√18 + 4√12 and show how to do it, please.

sciencesolve | Teacher | (Level 3) Educator Emeritus

Posted on

You should write the square roots such that:

`2sqrt(27) = 2*sqrt(3^3) = 2*sqrt(3^2*3) `

`2sqrt(27) = 2*(3^2)^(1/2)*3^(1/2) `

`2sqrt(27) = 2*3^(2/2)*3^(1/2) `

`2sqrt(27) = 2*3*3^(1/2) = 6sqrt3`

`2sqrt(27) = 6sqrt3`

`5sqrt8 = 5sqrt(2^3) = 5sqrt(2^2)^(1/2)*2^(1/2) = 5*2*sqrt2`

`5sqrt8 = 10sqrt2`

`3sqrt18 = 3*sqrt(2*3^2) = 3*2^(1/2)*3^(2/2) = 3*3*2^(1/2)`

`3sqrt18 = 9sqrt2`

`4sqrt12 = 4*sqrt(2^2*3) = 4*2^(2/2)*3^(1/2)`

`4sqrt12 = 8sqrt3`

Evaluating the expression yields:

`2sqrt(27) + 5sqrt8 - 3sqrt18 + 4sqrt12 =6sqrt3 + 10sqrt2- 9sqrt2 + 8sqrt3`

Factoring out `sqrt3 ` and `sqrt2`  yields:

`sqrt3*(6+8) + sqrt2(10-9) = 14sqrt3 + sqrt2`

Hence, evaluating the given expression yields `2sqrt(27) + 5sqrt8 - 3sqrt18 + 4sqrt12 = 14sqrt3 + sqrt2` .

Sources:

justaguide | College Teacher | (Level 2) Distinguished Educator

Posted on

The expression `2*sqrt 27 + 5*sqrt 8 - 3*sqrt 18 + 4*sqrt 12` has to be simplified.

`2*sqrt 27 + 5*sqrt 8 - 3*sqrt 18 + 4*sqrt 12`

=> `2*sqrt (9*3) + 5*sqrt (4*2) - 3*sqrt (9*2) + 4*sqrt (4*3)`

=> `6*sqrt 3 + 10*sqrt 2 - 9*sqrt 2 + 8*sqrt 3`

=> `14*sqrt 3 + sqrt 2`

The simplified form of `2*sqrt 27 + 5*sqrt 8 - 3*sqrt 18 + 4*sqrt 12` is `14*sqrt 3 + sqrt 2`