Converting to entire radicals to mixed radicals & Converting mixed radicals to entire radicals was what i had the most difficulty this whole unit. It was very confusing for me to convert as i would keep using the method for converting for one of them for the other one. I learnt that to convert entire radicals to mixed radicals, i’d have to multiply inside the radicand. It is a little confusing to explain in words so here is an example.

If i want to convert √108 to a mixed radical, 

√108 = √36 x 3               — I would find a number which can multiply into 108 that is square root

= √36 x √3            — I will separate it but it is still the same as √36 x 3

= 6 x √3                  — i will find the square root of 36 which is 6 and multiply it by √3

= 6√3                       — The answer is 6√3

To know if its the simplest form you have to make sure that the perfect square is the lowest perfect square it can be because or else it would not be the simplest form.

If i want to convert mixed radicals to entire radicals, i would need to bring the coefficient inside the radical number.

Ex. If i want to convert 3√14 to an entire radical,

3√14 = √3² x √14         — I would bring in 3 (coefficient) into the radical and square it

= √ 9 x 14            — therefore 3² = 9 so now we can multiply 9 x 14

= √126                  — the entire radical of 3√14 is √126

I still think i need to improve in this area but i now understand how to do it and i think i have really improved since i first started