How do you simplify radical expressions with variables?

1 Answer

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.