Why does my calculator show only one root?

Because the radical symbol is defined as the principal, positive root, so a function can return a single value. When you solve an equation rather than evaluate a symbol, both roots apply.

Is the square root of a negative number really impossible?

Not impossible, just not real. It is an imaginary number, which the quadratic solver on this site does handle.

Math & Statisticsalgebra

Square Root Calculator

The square root of a number, with the negative root shown alongside because both satisfy the equation. A negative input has no real square root and this says so rather than returning nothing.

Also called: sqrt calculator, root of a number.

Square root

The square root of 144 is 12. That is exact, so the number is a perfect square. The negative root is -12, and both are valid solutions of x squared equals 144.

Negative root

-12

Squared back, as a check

144

Cube root, for comparison

5.24

Is it exact

That is exact, so the number is a perfect square.

How this is calculated

Method and background

How this is calculated

The square root is the number that multiplied by itself gives the original. Every positive number has two: one positive and one negative, since a negative times a negative is positive. The radical sign conventionally means the positive one, which is why calculators show a single answer, but an equation of the form x squared equals nine has both three and minus three as solutions and dropping one is the classic exam mistake.

root = the number that multiplied by itself gives n

n: The number

Worked examples

Each of these is asserted on every build. If a change to the engine ever moved one of these answers, the build would fail before the page could print it.

a perfect square

Number: 144

Square root12

arithmetic identity

Open this example

an irrational root

Number: 2

Square root1.41

The classic irrational, to eight places

Open this example

the root of zero is zero

Number: 0

Square root0

degenerate case

Open this example

Method and limits

What it assumes

Real numbers only.

What it deliberately does not model

A negative input has no real square root. Its complex roots are outside this calculator.

Formula version 1.0.0 · definition 1.0.0 · United States · Report a problem with this calculator

Frequently asked questions

Why does my calculator show only one root?: Because the radical symbol is defined as the principal, positive root, so a function can return a single value. When you solve an equation rather than evaluate a symbol, both roots apply.
Is the square root of a negative number really impossible?: Not impossible, just not real. It is an imaginary number, which the quadratic solver on this site does handle.