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How do you simplify this: `sqrt(y^12)sqrt(z^18)` ? By the way the "y" and "z" are...

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rosey-girl | Student, Grade 12 | Valedictorian

Posted August 19, 2013 at 11:20 PM via web

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How do you simplify this: `sqrt(y^12)sqrt(z^18)` ?

By the way the "y" and "z" are together not separated.

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ncchemist | eNotes Employee

Posted August 19, 2013 at 11:58 PM (Answer #1)

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When you talk about square roots, you are really talking about raising something to the 1/2 power.  In other words, the exponent will be 1/2.  So first we need to convert the square roots for both variables (y and z) into numerical exponents that we can then simplify.

`sqrt(y^12)sqrt(z^18) = y^(12/2)z^(18/2)`

We can then simplify the fractions in the exponents to whole integers.

`y^(12/2)z^(18/2) = y^(6)z^(9)`

Since y and z are two distinct variables, this is the simplest form of the expression.

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