Rounding Square Roots Calculator with Steps and Graph

Calculator

Number Under the Square Root

Rounding Method

Decimal Places

Significant Figures

Graph Start

Graph End

Graph Step

Use decimal places or significant figures for custom precision. Use the preset rounding options for quick classroom and homework checks.

Plotly Graph

This graph shows the square root curve over your selected range. When a result exists, the exact point and the rounded point are highlighted.

Calculation History

This table keeps the latest results from the current browser session.

#	Time	Input	Exact Root	Rounded Root	Rule	Absolute Error	Relative Error
No results yet. Run a calculation to build the history table.

Example Data Table

Input	Exact Square Root	Rounding Rule	Rounded Result	Simplified Radical
2	1.4142135624	Nearest hundredth	1.41	√2
50	7.0710678119	Nearest thousandth	7.071	5√2
72	8.4852813742	2 decimal places	8.49	6√2
0.5	0.7071067812	3 decimal places	0.707	Available for non-negative integers only

Formula Used

1) Exact Square Root

r = √x, where x is the input number and r is the exact square root.

2) Rounded Value by Decimal Places

r_rounded = round(r, d), where d is the required number of decimal places.

3) Rounded Value by Significant Figures

r_rounded = round(r, s), where s is the required number of significant figures.

4) Absolute Error

Absolute Error = |r − r_rounded|

5) Relative Error Percentage

Relative Error % = (|r − r_rounded| / r) × 100

How to Use This Calculator

Enter the number you want under the square root sign.
Select a rounding method that matches your task.
Set decimal places or significant figures when needed.
Adjust the graph range to study nearby square root values.
Press the calculate button to show the result above the form.
Review the exact value, rounded value, bounds, and error measures.
Use CSV or PDF export to save a report.
Check the history table to compare several calculations.

Frequently Asked Questions

1) What does this calculator do?

It finds the square root of a non-negative number, rounds it with your chosen rule, and shows errors, bounds, a graph, and session history.

2) Can it round irrational square roots?

Yes. Most non-perfect squares have irrational roots. The calculator computes the exact decimal approximation, then rounds it using decimal places, significant figures, or preset levels.

3) What is the difference between decimal places and significant figures?

Decimal places count digits after the decimal point. Significant figures count meaningful digits from the first non-zero digit. Each method can produce different rounded results.

4) Why does the calculator show lower and upper squares?

They show the nearest perfect squares around your input. That helps you estimate the square root mentally and understand whether the rounded answer makes sense.

5) What is simplified radical form?

For non-negative integers, the calculator factors out the largest perfect square. For example, √72 becomes 6√2. This is useful in algebra and exact-form work.

6) Why are absolute and relative error helpful?

Absolute error shows the raw difference from the exact root. Relative error shows the difference as a percentage, making accuracy easier to compare across different inputs.

7) What does the graph show?

The graph plots y = √x over your chosen range. It also highlights the current exact point and the rounded point, so you can see the rounding effect visually.

8) What happens if the input is a perfect square?

The exact root is already a whole number, so rounding does not change it. The simplified radical form also becomes that whole-number root.