Simplify: 2√27 + 5√8 - 3√18 + 4√12 and show how to do it, please.
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calendarEducator since 2011
write5,348 answers
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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` .
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calendarEducator since 2010
write12,551 answers
starTop subjects are Math, Science, and Business
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`