Question

Radical expressions help??? Please!

A classmate simplified a radical expression below.
(1): Explain the error in this simplification.
(2): Show your work as you correct the error.

Answer 1

Explanation:

In order to add, subtract, multiply or divide the order of radicals (or Surds) must be equal.

(1) ERROR IN THE SIMPLIFICATION:

Order of radicals are not made equal

(2) CORRECT SOLUTION:

`= \frac{ \sqrt[7]{ {x}^(5) } }{ \sqrt[4]{ {x}^(2) } } \\ \\ = \frac{ \sqrt[7 * 4]{ {x}^(5 * 4) } }{ \sqrt[4 * 7]{ {x}^(2 * 7) } } \\ \\ = \frac{ \sqrt[28]{ {x}^(20) } }{ \sqrt[28]{ {x}^(14) } } \\ \\ = \sqrt[28]{ \frac{ {x}^(20) }{ {x}^(14) } } \\ \\ = \sqrt[28]{ {x}^(20 - 14) } \\ \\ = \sqrt[28]{ {x}^(6) }`