Questions about roots – especially higher order ones – are commonly asked during math tutoring.  The tutor offers a quick example.

Example: simplify ⁴√(80)

Step 1: Realize that 80=16(5). Therefore,

⁴√(80)=⁴√(16)⁴√(5)

Step 2: Realize that the reason we break 80 into 16(5) is that ⁴√(16)=2 (for the reason that 2x2x2x2=16). Therefore,

⁴√(80)=⁴√(16)⁴√(5)=2⁴√(5)

Most fourth roots cannot be simplified in this way; only those that contain a perfect fourth power (one of 2^4=16, 3^4=81, 4^4=256, etc) can be.

Example: Simplify ⁴√(1250)

Solution:

5^4=625. Therefore, we proceed as follows:

⁴√(1250)=⁴√(625)⁴√2=5⁴√(2)

Thanks for stopping by on this warm summer night:)

Jack of Oracle Tutoring by Jack and Diane, Campbell River, BC.