Radical question

Question

Express each entire radical as a mixed radical in simplest form

a) square root of 45

b) cube root of 40

c) square root of 243

Answer 1

The trick here is to be able to factor numbers.  If you can do that you're set.

 

Square root of 45, well first we factor 45 into primes and it is 5*9 or 5*3^2, therefore the square root of 45 is the square roof of (5*3^2)=square root of (5) *square root of (3^2) = squareroot(5)*3

The same goes for the other two problems, factor first and try to write out powers when you can since those are the parts of the radical that can be simplified.  For instance 40 is divisible by 8 which is 2^3, so you can be sure that there will be one whole number and a cube root of another number left over.