Square Root Calculator

Formula

Square root = sqrt(Nonnegative number)

Worked example

With Nonnegative number: 144, square root is 12.

Calculation method

The rule is Square root = sqrt(Nonnegative number).

For this square root example, changing nonnegative number from 144 to 145 while keeping the other inputs fixed changes square root from 12 to 12.041595.

Reading square root

The principal square root is nonnegative. A cube root can be negative when its input is negative. All four edges are equal and all four angles are right angles; a square therefore has more constraints than a general rhombus. In the worked values on this page, nonnegative number 144 produce square root 12.

Practical use

Use roots to recover a dimension from a squared or cubed quantity or solve a power relationship. The square rule applies to a four-sided figure with right angles, not just to any quadrilateral.

Limits and common mistakes

An even root of a negative number is not a real number. For a general nth-root calculation, keep the requested degree and domain clear. Check the right-angle assumption if a measured figure merely has four equal edges.

Why the relationship works

A square root reverses squaring for a nonnegative input. This calculator returns the principal, nonnegative root. If an equation says x squared equals a positive number, both positive and negative x may solve that equation even though the square-root function displays only the principal value. The square root rule uses nonnegative number in Square root = sqrt(Nonnegative number); read each symbol as the field named on this page.

Interpreting another set of values

For square root, the fields labeled nonnegative number are the known quantities. The calculator solves for square root using Square root = sqrt(Nonnegative number). The result may be an exact integer, a rounded decimal, an exponent, or a principal root. Preserve the original fraction or expression when a rounded display would lose precision needed later. When comparing two calculations, keep their units and input definitions identical.

For a second square root check, keep the other default inputs fixed and change nonnegative number from 144 to 146. Square root changes from 12 to 12.083046. This is a comparison of two particular cases. Repeat it near the values relevant to your task; do not assume that every formula changes at a constant rate.

Checks and limits

A real square root requires a nonnegative input. The displayed principal root is nonnegative, and rounding it before squaring it again can produce a small difference from the original number. The reported square root is 12 in the worked example. Keep its stated unit or counting convention when checking it against another calculation.