Write as a single radical expression. radicand 6x2 ^3radicand 3y.    radicand 6x2 ^3radicand 3y.

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durbanville | High School Teacher | (Level 2) Educator Emeritus

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  `sqrt (6 times 2) root(3)(3y)` 

Remember that roots convert to fraction equivalents so convert to powers  using laws of exponents:


`12^(1/2) times (3y)^(1/3)` 

Simplify the 12 to prime bases

= `(2^2 times 3)^(1/2) times (3y)^(1/3)`

The 2 can be simplified as `(2^2)^(1/2)` converts to 2 as the fraction exponent is `2/2 = 1` which is `2^1 = 2`

We need to have the same powers so that we can create one radical expression so use the common denominator (6) of the fraction exponents (powers). Remember we have already simplified the 2 so it can stand alone now:

`2. 3^(3/6) times (3y)^(2/6)`  

= `2 root(6)(3^3 times (3y)^2)`

Notice how the denominator is the root and the numerator is the power


`2 root(6)(27times 3^2 times y^2)` 

=`2 root(6)(243y^2)`