##### 4.1 Operations with radicals

The radical sign was said to be developed in 1500s in Germany. The radical ( sign was invented to find the root of a number, it can be a square root or the cube root, 4th root, 5th root etc., depending on the index of the radical sign.

Radicals can be evaluated and simplified like in the case of and they can also be converted from an entire radical, to a mixed radical or vice versa like in the case of . In converting radicals we need to apply our skills in factoring the perfect cubes or the perfect squares inside the radical sign.

We will also be learning how to evaluate radicals without the need to use calculator. There are a lot of times when there are fractions inside the radical, and there would also be times when there would be decimals. We will learn how to manually calculate them and also use a free radical calculator to check our answers.

There are also times when we will encounter the two kinds of radicals, which are the entire radicals like and the mixed radicals like. We would also be learning how to convert them into either entire radical to mixed radical or vice versa, by applying our knowledge of factoring out the perfect squares or the perfect cubes in the equation.

Each section of this chapter would discuss the topics mentioned above. It would be very useful to review the past concepts that we discussed about factoring, and radicals.