How to Find a Square Root on a Scientific Calculator

The square root of 144 is 12, because 12 times 12 is 144. On a scientific calculator you just type 144, hit the square root key (it looks like √, called the radical symbol), and 12 pops out. That's the whole trick — but the reason people search for it is that the key is never where you expect it, and the calculator sometimes answers a question you didn't ask.

Finding the Square Root Key

First, find the key. On most online scientific calculators it's right there on the face, marked √. On a physical one it's often a second function, so you press Shift or 2nd first, then the key with √ on it. Type the number first, then the key — 144, then √ — and you get 12. If your calculator works the other way round, key first then number, it'll still land on 12. Try it with a number you already know, like 81, before you trust it on homework: √81 is 9, and if you see 9, you're doing it right.

Perfect Squares and Endless Decimals

A square root is just the reverse of squaring. Squaring 12 gives 144; the square root of 144 gives you back 12. Numbers that come out even — 1, 4, 9, 16, 25, 36, 49, 64, 81, 100, 121, 144, 169 — are called perfect squares, and they're worth knowing because they turn up everywhere: a 12-by-12 patio is 144 square feet, and knowing √144 = 12 without reaching for anything feels good. For numbers that aren't perfect squares, the root is an irrational number — a decimal that never ends and never repeats. The square root of 2 is the famous one: type 2, hit √, and you get 1.41421356 and a trail of digits that never ends. That's normal. For homework, 1.414 is plenty. For a fence post or a shelf, 1.41 is plenty. The endless digits are the calculator being honest, not broken.

Estimating Without a Calculator

Estimating is a skill worth having when there's no calculator around. The square root of 50 sits between √49 (7) and √64 (8), closer to 7 — about 7.07, if you want the real value. The square root of 200 sits between 14 and 15, about 14.14. And if you ever need the diagonal of a square, that's just the side times √2: a 10-foot square has a diagonal of about 14.14 feet. That one fact has saved more fence projects than any other piece of math I know.

Two Keys That Cause Confusion

Two nearby keys cause confusion, so let's separate them. The cube root key (∛) asks "what number times itself three times gives this?" — the cube root of 27 is 3, not 9. And the x² key does the opposite of √: it squares. If you hit x² when you meant √, you'll get a huge number and a moment of panic. Also, the square root of a negative number isn't a real number at all — calculators will throw an error, and that's correct, not a malfunction.

Here's my own small confession: in school I once spent twenty minutes convinced my calculator was broken because sin(30) came out as -0.988 instead of 0.5. It wasn't broken — it was set to radians instead of degrees. Square roots don't have that trap, which is one reason they're a kinder place to start. But if your scientific calculator ever gives you a weird answer on trig, check that little DEG/RAD setting before you blame the machine. It's almost always that.

For anything else, the scientific calculator here does it in one tap, and it shows the steps for the trickier operations so you can see where the answer came from. I keep the free online calculators page open during homework season for exactly this kind of five-second check, and the math calculators cover the rest — fractions, triangles, all of it. When the next button on the calculator confuses you, all calculators are one click away.