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

Step-by-step 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:

$= \frac{ \sqrt[7]{ {x}^{5} } }{ \sqrt[4]{ {x}^{2} } } \\ \\ = \frac{ \sqrt[7 \times 4]{ {x}^{5 \times 4} } }{ \sqrt[4 \times 7]{ {x}^{2 \times 7} } } \\ \\ = \frac{ \sqrt[28]{ {x}^{20} } }{ \sqrt[28]{ {x}^{14} } } \\ \\ = \sqrt[28]{ \frac{ {x}^{20} }{ {x}^{14} } } \\ \\ = \sqrt[28]{ {x}^{20 - 14} } \\ \\ = \sqrt[28]{ {x}^{6} }$