Enter any positive number for instant bounds. See nearby perfect squares, decimal roots, and checks. Download clean results for study, homework, revision, or teaching.
| Number | Square Root | Lower Integer | Upper Integer | Statement |
|---|---|---|---|---|
| 7 | 2.645751 | 2 | 3 | 2 < √7 < 3 |
| 10 | 3.162278 | 3 | 4 | 3 < √10 < 4 |
| 26 | 5.099020 | 5 | 6 | 5 < √26 < 6 |
| 49 | 7 | 7 | 7 | √49 = 7 exactly |
| 80 | 8.944272 | 8 | 9 | 8 < √80 < 9 |
Let the input number be n.
Square root value: √n
Lower integer: floor(√n)
Upper integer: ceil(√n)
If k² < n < (k + 1)², then k < √n < k + 1.
If n is a perfect square, then √n is an exact integer.
Enter any non-negative number in the input field.
Press the calculate button.
The tool shows the decimal square root first.
It then shows the lower and upper integers around that root.
You also get the nearby perfect squares for quick verification.
Use the CSV option to save result data.
Use the PDF option to download a clean summary.
This calculator helps you find the two integers around a square root. It is useful when you need fast interval checks in maths. Enter a non-negative number, and the tool computes the decimal root immediately. It also identifies the lower integer, upper integer, and nearby perfect squares. This makes comparison simple and clear.
Many school and exam questions ask where a square root lies. Students often need to decide whether a root is between 3 and 4, 8 and 9, or some other pair. This page removes guesswork. It uses the actual square root value, then applies floor and ceiling logic. That gives correct integer bounds every time. The result is easy to read and easy to verify.
You can use this tool for homework, revision, worksheets, and classroom work. It is also helpful when checking mental estimates. For example, if a number is between 25 and 36, then its square root must be between 5 and 6. The calculator shows that pattern clearly. It also marks perfect squares, so you know when the answer is exact instead of estimated between two integers.
The result section appears above the form after submission. That keeps the answer visible right away. The example data table shows how different numbers behave. The formula section explains the rule in plain language. The export options also make this page practical. You can save a CSV for records or download a PDF for study notes. Overall, this square root interval calculator is a simple way to learn, verify, and present root bounds with confidence.
It finds the two integers around the square root of a non-negative number. It also shows the decimal root, nearby perfect squares, and whether the number is a perfect square.
Yes. The calculator accepts non-negative decimals. It still computes the square root and shows the lower and upper integers around that value.
If the number is a perfect square, the square root is exact. In that case, the lower and upper integers are the same exact root.
They help you estimate square roots quickly. This is common in maths exercises, number sense practice, and exam questions that ask for bounds.
The tool compares the input with nearby perfect squares. If the number lies between k² and (k+1)², then its square root lies between k and k+1.
Yes. The square root of zero is zero. The result shows an exact integer root because zero is a perfect square.
The CSV file saves the result in a spreadsheet-friendly format. It is useful for record keeping, worksheets, and sharing simple numeric outputs.
The PDF contains a clean summary of the current result. It includes the input, root value, integer bounds, nearby perfect squares, and the final statement.
Important Note: All the Calculators listed in this site are for educational purpose only and we do not guarentee the accuracy of results. Please do consult with other sources as well.