How to Find the Smallest Index of Square Roots With Exponents

Indices denote the operation to be performed.

The index of any root, whether it is a square root, cube root or fifth root, is the number of times that root must be multiplied by itself to get the original starting number. Any easy example is for a cube root: 64 is 4x4x4, or 4 cubed. The cube root of 64 is 4, and because we need to multiply 4 times itself 3 times, we say that the index of the cube root is 3.

Instructions

1. Solve the square root; i.e. if you are given 16 the square root is 4.

2. Multiply the answer from Step 1 by itself until you reach the original answer; i.e. if your answer is 4 multiply 4 by itself until you get 16.

3. The number of times you multiplied your root times itself in Step 2 is the index; i.e. if your root is 4, you would have multiplied 4x4 to get 16, so your index is 2.

References

• Purple Math: Radicals