Roots of Real Numbers 1 2 3 Definitions Simplifying Radicals Practice Problems

Definition Square Root Cube Root nth Root Base number of a value taken to the second power Example: the square root of 49 is ±7, since (±7)2=49 Cube Root Base number of a value taken to the third power Example: the cube root of 125 is 5, since 53=125 nth Root Base number of a value taken to any power Example: the 8th root of 256 is 2, since (±2)8=256

Nominclature

Rules Positive numbers Negative numbers Odd index number means Roots are always positive Even index numbers means Roots are both positive and negative Example: since both 4 and -4 squared will result in 16 Negative numbers Even index number, no real root Odd index number, always negative Example:

Finding Roots