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Simplify 5k-2 the square root of 2k^4 divided by the square root of 5k^3.

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rosey-girl | Student, Grade 12 | (Level 1) Valedictorian

Posted January 28, 2013 at 4:02 AM via web

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Simplify 5k-2 the square root of 2k^4 divided by the square root of 5k^3.

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embizze | High School Teacher | (Level 1) Educator Emeritus

Posted January 28, 2013 at 4:41 AM (Answer #1)

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Simplify `(5k-2sqrt(2k^4))/(sqrt(5k^3))`

`=(5k-2sqrt(k^4)sqrt(2))/(sqrt(k^2)sqrt(5k))`

`=(5k-2k^2sqrt(2))/(ksqrt(5k))`

`=(5-2ksqrt(2))/(ksqrt(5k))` multiply numerator and denominator by ``

`=(5sqrt(5k)-2ksqrt(10k))/(5k^2)`

`=(sqrt(5k)(5-2ksqrt(2)))/(5k^2)`

which is simplified.

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