³√(27y 3 ) ⁄ √(27y 2 ) =

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Accepted Answer

The cube root of 27y 3 = 3y, since (3y)(3y)(3y) = 27y 3 . Factor the denominator into two radicals: √(27y 2 ) = √(9y 2 ) · √3. The square root of 9y 2 = 3y, since (3y)(3y) = 9y 2 . The expression is now equal to 3y ⁄ 3y√3 . Cancel the 3y terms from the numerator and denominator, leaving 1 ⁄ √3 . Simplify the fraction by multiplying the numerator and denominator by √3: ( 1 ⁄ √3 )( √3 ⁄ √3 ) = √3 ⁄ 3 .

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