Square Root on a Calculator: Step-by-Step

This guide shows you how to enter a square root on a standard scientific calculator, a basic calculator, and a phone app. You’ll learn which button to press, in what order, and how to read the result correctly. No special tools are needed beyond the calculator itself.

Formula

The square root of a number x is written as √x and is the value that, when multiplied by itself, gives x. In formula form:

√x = y where y × y = x

For example, √25 = 5 because 5 × 5 = 25. The number under the root sign (x) is called the radicand. The result (y) is the square root. Every positive number has two square roots: one positive and one negative. The calculator’s √ button returns the principal (positive) root.

Worked Example

Using the default value of 25 from the calculator above:

1. Identify the radicand: x = 25.
2. Press the √ button on your calculator.
3. Enter 25.
4. Press the equals (=) button.
5. The display shows 5.

Check: 5 × 5 = 25, so the answer is correct.

What You’ll Need

• A scientific calculator (physical or app) with a √ button – most phones have this in their calculator app when rotated to landscape.
• A basic calculator – these often lack a √ button, but you can use the method described in Step 4.
• Alternatively, a computer with a web browser – you can use the built-in calculator or an online one.

Step-by-Step

1. Turn on your calculator and clear any previous calculation by pressing the AC (All Clear) or C (Clear) button.
2. Find the √ button. On most scientific calculators, it is a dedicated key, often yellow or above another key, requiring a shift or 2nd function press. On phone apps, it may be hidden in a second page of symbols.
3. Press the √ button first (on most scientific calculators). This tells the calculator you want a square root.
4. Enter the number you want the square root of. For example, type 144.
5. Press the equals (=) button. The calculator will display the result – for 144, it shows 12.
6. If your calculator does not have a √ button (common on basic models), use the exponent method: type the number, press the “x^y� or “^� button, then type 0.5, and press equals. This works because √x = x^(1/2).
7. On a phone calculator app, rotate the phone to landscape to reveal scientific functions. Look for the √ symbol, often near the number pad.

Common Mistakes

• Pressing the number before the √ button – on most scientific calculators, this gives the square root of that number, but on some it may be interpreted differently. Always test with a perfect square like 25 to see which order works.
• Forgetting to close parentheses when using the √ inside a longer expression, e.g., √(9+16) – if you type √9+16, you get 3+16=19 instead of √25=5.
• Using the wrong exponent – some people type ^2 instead of ^0.5 when using the exponent method. That squares the number instead of taking the root.
• Ignoring the negative root – the calculator gives the positive root only. If you need the negative root, put a minus sign in front of the result.

Tips

• Always test your calculator with a known perfect square (like 9, 16, 25) before trusting the result for a new number.
• If you need the square root of a decimal or fraction, the same steps work – just enter the decimal point or fraction as usual.
• For very large numbers, the calculator may display the result in scientific notation (e.g., 1.4142e+1 for √200). That means 1.4142 × 10¹ = 14.142.
• Use the “2ndâ€� or “shiftâ€� key if the √ symbol is printed above another button – this is common on graphing calculators.
• When working with negative numbers, remember that the square root of a negative number is not a real number – the calculator will show an error. You need to use imaginary numbers (i) for that.

Troubleshooting

• Error message when pressing √: You likely entered a negative number. The square root of a negative number is not a real number. If you need the imaginary root, multiply the result by i (e.g., √(-9) = 3i).
• Wrong answer: Check if you pressed the √ button before or after the number. Try the opposite order. Also check if you have a “2ndâ€� or “shiftâ€� function active – that may change the button’s meaning.
• No √ button at all: Use the exponent method (x^0.5). On Windows calculator, switch to “Scientificâ€� mode (View > Scientific). On iPhone, rotate to landscape. On Android, swipe left on the calculator screen to reveal more functions.
• Result is a long decimal: That’s normal for non-perfect squares. You can round to a specific number of decimal places, or use the “FIXâ€� or “SCIâ€� display settings on your calculator.
• Calculator shows “Math Errorâ€� or “Domain Errorâ€�: This usually means you tried to take the square root of a negative number, or the number is too large for the calculator’s capacity.

Frequently Asked Questions

Q: Do I press the √ button before or after the number?
A: On most scientific calculators, press √ first, then the number, then equals. On some basic models, you type the number first, then press √. Test with a perfect square to see which order your calculator uses.

Q: How do I find the square root on a phone calculator?
A: Rotate your phone to landscape mode – most phone calculators then show scientific functions including √. If that doesn’t work, look for a “sciâ€� or “advancedâ€� button in the app.

Q: Can I calculate a square root without a √ button?
A: Yes. Use the exponent method: type the number, press the “^� or “x^y� key, type 0.5, and press equals. This works because the square root is the same as raising to the power of one-half.

Q: Why does my calculator give a negative answer for a square root?
A: It shouldn’t – the principal square root is always positive or zero. If you see a negative, you may have entered a negative number or used the wrong key. Some calculators have a separate “negativeâ€� button – make sure you’re using the correct one.

Q: What is the square root of 0?
A: The square root of 0 is 0, because 0 × 0 = 0. Any calculator will show 0.

Q: How do I take the square root of a fraction?
A: Enter the fraction as a decimal (e.g., 1/4 = 0.25) and then take the square root. Or, if your calculator has a fraction key, enter the fraction and then press √. For 1/4, the square root is 0.5.

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in x | Number | - | 25 | 0
out sqrt | Square root | - | sqrt(x) | 4