Root Calculator
Square root, cube root, or any nth root.
Roots are fractional exponents
The nth root of x is x^(1/n). √50 ≈ 7.0711, and the cube root of 50 is about 3.684. Odd roots accept negative numbers (the cube root of -8 is -2); even roots of negatives leave the real numbers, which is where i comes in.
Estimating by hand
Square roots sit between the nearest perfect squares: 50 lies between 49 and 64, so √50 is a hair above 7. One round of the ancient Babylonian method sharpens it: average 7 and 50/7 to get 7.0714, already correct to three decimals.