Calculate a square root
Get an exact estimate and a correctly rounded tenths result.
Formula used
For a nonnegative number n, first calculate the principal root r = √n.
The formula keeps one digit after the decimal point. It uses normal half-up rounding. Values ending in five or more at the hundredths place round upward.
How to use this calculator
- Enter a zero or positive number in the Number field.
- Select a decimal separator that matches the number entered.
- Choose how many digits you want in the exact estimate.
- Turn result details on or off with the optional checkboxes.
- Select Calculate nearest tenth to see the result above the form.
- Use the CSV or PDF buttons to save a completed calculation.
Example values
| Number | Square root estimate | Nearest tenth | Check |
|---|---|---|---|
| 2 | 1.414214 | 1.4 | 1.4² = 1.96 |
| 20 | 4.472136 | 4.5 | 4.5² = 20.25 |
| 81 | 9.000000 | 9.0 | 9.0² = 81.00 |
| 150 | 12.247449 | 12.2 | 12.2² = 148.84 |
Accurate Square Root Rounding
A square root identifies the number that produces a value when multiplied by itself. For example, the square root of 81 is 9 because 9 × 9 equals 81. Rounding to the nearest tenth gives a readable answer.
This calculator accepts whole numbers and decimals. It finds the principal square root automatically. It then checks the first decimal place and applies standard half-up rounding. The rounded answer always shows one decimal digit. This format works well for schoolwork, measurements, estimates, and quick checks.
Why the Nearest Tenth Matters
A tenth is the first digit after the decimal point. To round a square root to tenths, inspect the hundredths digit. Keep the tenths digit when that digit is zero through four. Increase the tenths digit by one when it is five through nine.
Consider √20. Its unrounded value is approximately 4.4721. The tenths digit is 4. The hundredths digit is 7. Because 7 is at least 5, the tenths digit increases. Therefore, √20 rounded to the nearest tenth is 4.5. The calculation details make this result easier to verify.
Using Decimals and Larger Values
You can enter a decimal value such as 2.25. The exact square root is 1.5, so the tenth result is 1.5. For instance, √12,544 is 112.0. The calculator flags perfect squares when the root is a whole number.
Choose the decimal separator that matches your entry. Dot mode accepts formats like 12.75. Comma mode accepts formats like 12,75. The page also offers a precision setting for the unrounded display. This setting does not change the nearest-tenth answer. It only controls how many detail digits appear.
Reading the Calculation Details
The result panel shows the supplied value, the calculated root, and the nearest-tenth answer. It also displays the adjacent tenth values. These values show where the exact root sits before rounding. The verification value squares the rounded result. It helps explain why a rounded number may not exactly recreate the original input.
Perfect squares need little interpretation. Their roots are exact integers. Other values require an estimate. A close estimate is often enough for planning or checking. Use more displayed digits when you need to inspect the rounding step. Keep the final tenths value when a simple reported answer is required.
Helpful Checks Before You Submit
Only zero and positive values have real square roots. Negative inputs generate a clear message instead of an incorrect answer. Avoid letters or empty fields. Confirm that your chosen separator matches the number you typed. This prevents common formatting mistakes.
Remember that rounding happens after calculating the root. Do not round the original number first unless a question specifically requests it. Early rounding can change the final answer. Use the exported report when you need to save your calculation. It records the input, exact estimate, rounded result, and selected settings.
Frequently asked questions
1. What does nearest tenth mean?
It means keeping one digit after the decimal point. The second decimal digit decides whether the first decimal digit stays the same or increases by one.
2. Can I enter a decimal number?
Yes. Enter a positive decimal such as 2.25 or 12.75. Select comma mode when your decimal number uses a comma instead of a dot.
3. Why is the rounded result not exact after squaring?
Rounding changes the root slightly. Squaring the rounded value can produce a nearby value instead of the original number. The exact estimate remains more precise.
4. What happens with a perfect square?
A perfect square has a whole-number root. For example, √81 equals 9 exactly. The calculator still displays the tenths version as 9.0.
5. Can this calculator find negative square roots?
No. This page calculates the principal real square root. Negative numbers do not have real square roots, so the calculator requests zero or a positive input.
6. Which digit controls tenths rounding?
The hundredths digit controls it. A hundredths digit from 0 through 4 keeps the tenths digit. A digit from 5 through 9 raises it.
7. Does changing exact estimate digits alter the answer?
No. That option only changes the displayed detail for the unrounded root. The calculator always rounds the calculated root to one decimal place.
8. Can I use scientific notation?
Yes. Choose scientific notation for the exact estimate display. The nearest-tenth result remains easy to read in standard decimal notation.
9. Why choose a decimal separator?
The choice tells the calculator how to read your value. It prevents confusion between commas used for decimals and commas used for thousands.
10. Are CSV and PDF reports included?
Yes. After a successful calculation, use the download buttons in the result panel. Each report includes the input, root estimate, rounded tenth, and verification details.
11. Is zero a valid input?
Yes. The square root of zero is zero. The nearest-tenth result will display as 0.0.