Utilorca

Square root calculator

Square root calculator by Utilorca (utilorca.com): free, no sign-up, runs in your browser. Get the square root of any number to 10 decimal places, the simplified radical form, and between which perfect squares it falls. Switch to cube or any root up to the 10th.

Perfect squares from 1 to 30

1²12²43²94²165²256²367²498²649²8110²10011²12112²14413²16914²19615²22516²25617²28918²32419²36120²40021²44122²48423²52924²57625²62526²67627²72928²78429²84130²900

Perfect cubes from 1 to 15

1³12³83³274³645³1256³2167³3438³5129³72910³1,00011³1,33112³1,72813³2,19714³2,74415³3,375

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How to use it

  1. Type the number (decimals and negatives work).
  2. Pick the root: square, cube or up to the 10th.
  3. Read the decimal result, the simplified radical and the check.

Questions and answers

How do you simplify a square root?

Split the number into a perfect square times what is left and take the square root of the perfect square: √72 = √(36 × 2) = 6√2.

Can you take the square root of a negative number?

Not among real numbers. In complex numbers √−16 = 4i, where i is the imaginary unit (i² = −1). Odd roots of negatives are fine: ∛−27 = −3.

How do I estimate a square root by hand?

Find the two perfect squares around it: 50 is between 49 (7²) and 64 (8²), so √50 is a little more than 7 (it is about 7.07).