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algebra multiply radicals

Simplify the following radical expression

problem radical 3y(radical27y3 - radical y)

show how to multiply an expression containing radicals

Comments for algebra multiply radicals

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Apr 07, 2011
Simplify Radical Expression
by: Staff

The question:

problem radical 3y(radical27y3 - radicaly)

The answer:

problem radical 3y(radical27y3 - radicaly)

= 3y[√(27y3) - √(y)]

Multiply factors under the first radical

= 3y*[√(27*y*3) - √(y)]

= 3y*[√(81*y) - √(y)]

Identify any squared factors under the first radical (there is only 9²)

= 3y*[√(9²*y) - √(y)]

Although it is an extra step, factor the first radical into two radicals which are multiplied together. This will make it easier to follow the simplification process.

= 3y*[√(9²)*√(y) - √(y)]

Evaluate √(9²): √(9²) = 9

= 3y*[9*√(y) - √(y)]

Combine like terms within the brackets [ ]: 9*√(y) - √(y) = 8*√(y)

= 3y*[8*√(y)]

Multiply remaining factors

= 3*8*y*√(y)

= 24*y*√(y)

= 24y√(y)

The final answer is: 24y√(y)

Thanks for writing.


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