Simplified Form of A Radical Expression
A radical expression is said to be in simplified form if
- There is no factor of the radicand that can be written as a power greater than or equal to the index.
- There are no fractions under the radical sign.
- There are no radicals in the denominator.
For example, to write the radical expression in simplified form, we can proceed as follows. First, look for a perfect square under the square root sign and remove it:
Next, there is a fraction under the radical sign, which we change as follows:
Finally, we remove the radical from the denominator as follows:
When there is a denominator involving surds it may be possible to find a factor to multiply both numerator and denominator by to simplify the expression. For instance using the factorization of the sum of two cubes:
Simplifying radical expressions involving nested radicals can be quite difficult. It is not immediately obvious for instance that:
Read more about this topic: nth Root
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