Find square roots, cube roots and nth roots to up to 100 exact decimal places, with radical form. Runs on your device.
The square root of a number is the value that gives the number when multiplied by itself, so √72 is about 8.4852813742 and equals 6√2 in simplest radical form. The page opens with 72: the radical is 6√2, the decimal is 8.4852813742, and the answer lies between 8 and 9 because 8² = 64 and 9² = 81. Pick Cube root, 4th root, 5th root or any index from 2 to 50. The decimal places can be set from 0 to 100, and a table lists the perfect powers around your number, such as 36, 49, 64, 81, 100 and 121 for 72. Under the answer a line asks whether your number is a perfect square, cube or higher power, and says what it is a power of when it is.
To simplify a root, take out the largest perfect power that divides the number. For √72, 72 = 36 × 2 and 36 = 6², so √72 = 6√2. For a cube root, ∛54 = ∛(27 × 2) = 3∛2, because 27 = 3³. A whole number that is a perfect power gives a whole answer: √144 = 12 and ∛125 = 5. If no square factor above 1 exists, as in √10, the radical is already simplest. The page does this for whole numbers up to 9,007,199,254,740,991; decimals such as 12.5 get the decimal answer only.
Ordinary floating-point numbers hold about 16 digits, so a root asked for to 30 places would be mostly noise. This page computes the root with whole-number arithmetic instead, so every digit you ask for is right, and the last one is rounded half up. √2 to 20 decimal places is 1.41421356237309504880. If the root ends, the page shows it in full: √2.25 = 1.5, and the perfect-power line says so. A number may have up to 15 digits before the decimal point and at most 60 decimal places, and a number you type is used as typed, so 0.1 is exactly one tenth.
No real number squared is negative, so the square root of a negative number is imaginary. The page shows √−18 as 3i√2, about 4.2426406871i, where i² = −1. A cube root or any odd root of a negative number is real and keeps the sign: ∛(−27) = −3. An even root above 2, such as the 4th root of −16, has no real value; the page says so and gives the principal complex root, rounded to 8 decimals. It shows principal roots only, not every complex root, and it does not solve equations. For equations with x² in them, use the quadratic formula calculator.
Find the largest square that divides the number and take its root outside. For √72, 72 = 36 × 2, so √72 = 6√2. For √50, 50 = 25 × 2, so √50 = 5√2. Type the number and the page shows the radical beside the decimal.
1.4142135624. The page shows more if you ask for it: to 20 places √2 is 1.41421356237309504880. It is irrational, so the digits never end or repeat, and the last digit shown is rounded.
Choose Cube root and type the number. ∛27 = 3 because 3 × 3 × 3 = 27, and ∛54 = 3∛2, about 3.7798. A negative number works: ∛(−8) = −2.
Not as a real number. The page gives the imaginary answer: √−4 = 2i and √−18 = 3i√2, with i meaning √−1. Every negative number has two square roots, ±; the page shows the principal one with i positive.
Its square root is a whole number. 144 is a perfect square because √144 = 12, while 150 is not because √150 lies between 12 and 13. The page answers the question and lists the squares nearby.
No. The numbers are processed in your browser and are not uploaded. They are not stored on your device either, and reloading the page puts the 72 example back.