How to Compute the Square Root on a Mac

Looking for the square root of 2? Got a formula figured out and there’s something squared on one side? Find out here how to compute the square root (and other roots) for a number quickly on a Mac (using Spotlight, Calculator or Terminal).

First, 265 Feet Down, Waters Above and Waters Below

It’s some 80 meters or 265 feet, they tell you, looking down into the shallow waters of the Gardon river from atop a famous aqueduct. Up here, shallow waters would be on their way to the prosperous city gates of Nîmes.

What were to happen, now, if from the drops above one were to join its kin below? How fast would it be at the end of its journey?

That’s easy, I hear you say, of course: $v=\sqrt{2gd}$, with Earth’s gravitational acceleration $g\approx 9.81m/s^2$ at some 70 meters above sea level and the distance $d=80m$.

So, let’s find out how to calculate that square root of about 1570 for the impressive speed (in m/s):

How to Compute the Square Root for a Number on a Mac

Using Spotlight

it’s also for writing: How to Insert the Square Root Symbol ( √ ) on a Mac

Compute Other Roots with Spotlight

You can also compute other roots than the square root with Spotlight.

To take arbitrary roots most easily on a Mac:

1. Bring up Spotlight search.
2. Type <radicand> ^ (1 / <index>).
   Radicand: Replace <radicand> with the number whose root you want to take.
   Index: Replace <index> with the index of the radical, e.g., 3 for a cube root.
   Raising: ^ is, of course, the operator that will raise (e.g. square) a number in Mac Spotlight.
   Examples: Type 27 ^ (1 / 3) for the cube root of 27 (3), or 9 ^ (1 / 2) for the equivalent of the square root of 9 (also 3).

Mac Spotlight Square Root Example

Type sqrt((34.6+4)^3/5) in Spotlight to compute $\sqrt{\frac{{(34.6+4)}^3}{5}}$.

Compute a Root Using Mac Calculator

To use macOS Calculator to find the square root (or the nth root) for any number:

1. Open Calculator.
   Here’s how: You can use Launchpad to open Calculator, for example.
2. Switch to Scientific mode.
   Here’s how: Press Command 2 in Calculator or select View | Scientific from the menu.
3. Enter the number whose square root you want compute.
   Type-or-press: You can either use the on-screen buttons or the keyboard to enter the number.
4. Click $\text{exception 25:}$.
   Other radices: Press $\text{exception 25:}$ for the cube root and $\text{exception 25:}$ followed by the root’s index for an nth root.
   

Calculate Square Roots in Mac Terminal

To compute the root for a number fast on a Mac using bc in Terminal:

1. Open Terminal on the Mac.
2. Type bc -e "sqrt(<radicand>)" for the square root.
   Cube root: Use bc -e "cbrt(<radicand>)" to compute the cube root.
   Nth root: You can use bc -le "root(<radicand>, <n>)" to take the nth root of the radicand.
   Examples: Use bc -e sqrt(9) to quickly compute the square root of 9 and bc -le "root(243, 5)" to compute the 5th root of 243.
   Why “-l”: The -l parameter loads the math library for bc, which includes the root() function for computing arbitrary roots.
3. Press Enter.
   

(How to compute the square root for a number on a Mac tested with macOS Sonoma 14.3; updated April 2024)