Without using a calculator of any kind, figure out which is the larger root:

- Square root of 2
- Cube root of 3

#### Solution

Cube root of 3.

Take both and raise them to the power of 6:

- (Square root of 2)^6 = 2^3 = 8
- (Cube root of 3)^6 = 3^2 = 9

Since 9 > 8, and we raised both expressions to the same (even) power, cube root of 3 must be the larger root.

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