Simplest Form Radicals

Question 1

What are radicals, roots, and surds?

Answer 1

They’re basically all the same thing. The difference between them is not important.

They are numbers that have this symbol:

Question 2

What does “simplest form” mean for square roots?

Answer 2

It means you have to factorise the number and try to extract as many “perfect” squares as you can.

1. Factorise the number to primes and factor out as many squares from variables as you can.
2. Extract the perfect squares
3. Multiply out the stuff outside the root and the stuff inside the root (separately).

For example:

Question 3

Write the following in simplest form:

Answer 3

1. Factorise the number to primes and factor out as many squares from variables as you can.
2. Extract the perfect squares
3. Multiply out the stuff outside the root and the stuff inside the root (separately).

Question 4

Write the following in simplest form:

Answer 4

1. Factorise the number to primes and factor out as many squares from variables as you can.
2. Extract the perfect squares
3. Multiply out the stuff outside the root and the stuff inside the root (separately).

Question 5

What does “simplest form” mean for cubed roots?

Answer 5

It means you have to factorise the number and try to extract as many “perfect” cubes as you can.

1. Factorise the number to primes and factor out as many cubes from variables as you can.
2. Extract the perfect cubes.
3. Multiply out the stuff outside the root and the stuff inside the root (separately).

For example:

Question 6

Write the following in simplest form:

Answer 6

1. Factorise the number to primes and factor out as many cubes from variables as you can.
2. Extract the perfect cubes.
3. Multiply out the stuff outside the root and the stuff inside the root (separately).