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SnapCalculations

Square Root Calculator

Enter a number to get its square root (or cube or nth root) as a decimal and in simplest radical form, such as √72 = 6√2.

√72

8.48528137

Simplest form: 6√2

Simplest radical form
6√2
Check: answer^2
72

Step-by-step solution

Worked out with your numbers. Change any value above and the steps update.

  1. 1

    Break the number into prime factors

    72 = 2³ × 3²

  2. 2

    Take one factor out of each of the pairs

    outside: 6, left inside: 2

  3. 3

    Simplest form

    √72 = 6√2

  4. 4

    As a decimal (rounded to 8 places)

    6 × √2 = 8.48528137

How it works

  • Break the number into prime factors, for example 72 = 2³ × 3².
  • For a square root, every pair of equal factors comes out as one factor; cube roots take triples, and so on.
  • What is left inside stays under the root sign: √72 = 2 × 3 × √2 = 6√2.
  • The decimal value is the number raised to the power 1/n.

Frequently asked questions

Can I take the square root of a negative number?

Not as a real number. Cube roots and other odd roots of negative numbers do exist, for example ∛−27 = −3.

Which numbers can be simplified?

Whole numbers up to one trillion are simplified exactly. Decimals are shown as a decimal value only.

Results are estimates for general information and are not financial, medical or professional advice.