E. Mixed Radical Conversions

Converting a mixed radical to an entire radical is also a valuable math skill. Recall the relationship between a radical with a perfect square or perfect cube radicand and its whole number equivalent.

Analyzing more square roots of perfect squares and cube roots of perfect cubes will help create recognizable patterns.

The patterns:

  • For square roots, squared factors under the root sign are apparent, such as .

  • The square root and the exponent 2 undo each other because squaring and taking the square root are opposite operations, much like multiplying and dividing.

  • For cube roots, cubed factors under the root sign are apparent, such as .

  • The cube root and the exponent 3 undo each other because cubing and taking the cube root are opposite operations.

These observations can be used to convert mixed radicals into entire radicals.