Question

How do you simplify radical expressions with variables?

Answer 1

This is easy! If you want to multiply this are the rules: First coefficients are multiplied with each other and the sub-radical amounts each other, placing the latter product under the radical sign common and the result is simplified.

Let's go: `2sqrt5` times `3sqrt10`

`2sqrt5 × 3sqrt10 = 2 × 3sqrt(5×10)=6sqrt50`

`= 6sqrt(2·5^2)`

`= 30sqrt2`

Now if you want to divide, then the coefficients are divided among themselves and sub-radical amounts each other, placing the latter quotient under the radical common and the result is simplified.

`2root3 (81x^7)` by `3root3( 3x^2)`

`(2root3 (81x^7)) /(3root3 (3x^2)) = 2/3root3 ((81x^7)/(3x^2)) =2/3root3 (27x^5)`

`2/3 root3 (3^3·x^3·x^2) = 2xroot3 (x^2)`

I hope you can find it useful, and here is a link to solve this ones with different indices.