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Rational Exponents and Radicals

Rational Exponents and Radicals 1.7 - Solution

arrow_back Return to Rational Exponents and Radicals

Before dividing the given radical expressions, we need to answer two questions.

  1. Can the expressions be divided?
  2. If so, do absolute value symbols need to be added to the answer?
The rule regarding dividing radical expressions states that if and are real numbers and then Because we are assuming that both radicals are real numbers and we can see that the given expressions have the same index, we can divide them. Now, to answer the second question, consider the rule regarding absolute value symbols. Because our radicals have an odd root, negative numbers will not cause the expressions to be imaginary. Therefore, we don't need to worry about absolute value symbols.
Simplify
Next, let's simplify the radical expression by finding all of the perfect cubes inside the radical.
Let's stop here for a moment and consider the fact that we need to have a rationalized denominator. If we simplified all of the perfect cubes as they are, we would be left with in the denominator. To avoid this, we can multiply the numerator and denominator by a factor that will create a perfect cube, which in this case is
Simplify