How to use this calculator
Enter any number and click Calculate. You will see the square root as a decimal, whether the number is a perfect square, the simplified radical form (for example, the square root of 72 simplifies to 6 times the square root of 2), and the two nearest perfect squares above and below your number.
The calculator also shows the cube root automatically. If you want a different root (4th root, 5th root, etc.), change the Nth root field before calculating.
Understanding simplified radical form
A radical is simplified when there are no perfect square factors left inside the radical sign. To simplify, find the largest perfect square that divides evenly into your number, take its square root outside, and leave the remainder inside.
For example, the square root of 72: since 36 times 2 equals 72, and the square root of 36 is 6, we get 6 times the square root of 2. This is useful in algebra when you need exact answers instead of decimal approximations.
Frequently asked questions
What is a square root?
A square root of a number is a value that, when multiplied by itself, produces the original number. The square root of 25 is 5 because 5 times 5 equals 25. The radical symbol (√) represents the square root operation.
How do you calculate a square root by hand?
Use the estimate and average method. Start with a guess, divide the original number by your guess, then average the result with your guess. Repeat until you reach the desired precision. Each iteration gets you closer to the true square root.
What is a perfect square?
A perfect square is a number whose square root is a whole number. Examples: 1, 4, 9, 16, 25, 36, 49, 64, 81, 100, 121, 144, and so on. These are the results of multiplying any integer by itself.
What is the difference between square root and cube root?
A square root asks "what number times itself equals this?" A cube root asks "what number times itself three times equals this?" The cube root of 27 is 3 because 3 × 3 × 3 = 27. Unlike square roots, cube roots can be calculated for negative numbers.