How to use the square and cube root calculator
This calculator finds the square root and the cube root of a number at the same time, and where possible it also tidies the radical into exact form. Entering 72 gives a square root of about 8.48528137, exactly 6โ2, and a cube root of about 4.16016765, exactly 2โ9.
Negative input behaves differently for the two roots. A cube root of a negative number is real, so โ8 returns โ2, while a square root of a negative number has no real value and is reported with the imaginary unit i instead. Entering 0 gives 0 for both roots.
Exact forms appear only when the input is a whole number with absolute value up to one billion. Square and cube factors are pulled outside the radical so that โ72 becomes 6โ2 and โ16 becomes 2โ2, and when nothing is left inside the value is reported as a perfect square or a perfect cube.
Irrational roots cannot be written exactly as finite decimals, so results are shown to eight decimal places and whole-number checks use a tolerance of 1e-9. The reverse-check line squares the square root and cubes the cube root again, letting you confirm that both return to the number you entered.
Frequently Asked Questions
Yes. A negative number has a real cube root, so the cube root of โ8 is โ2. Raising โ8 to the power 1/3 with an ordinary power function fails, but this calculator uses a dedicated cube-root operation and returns exactly โ2.
No real number squares to a negative value. When you enter a negative number the calculator says there is no real answer and shows the size of the root with the imaginary unit i instead.
Whenever the input is a whole number with absolute value up to one billion. Square factors are pulled out so โ72 becomes 6โ2, and cube factors so โ72 becomes 2โ9. For decimal input those lines are hidden.