1
Enter the radicand
Type the number inside the square-root or nth-root symbol.
Free Square Root Calculator
A square root calculator finds the value that produces a number when multiplied by itself. Calculate square roots and nth roots, simplify radicals, and follow each step.
SPED math support
Use the steps to support differentiated instruction
Enter relevant goals and accommodations manually in the lesson planner. Calculator results are not transferred, and lesson drafts should be reviewed before use.
Radical and nth-root calculator
Enter a number and root index
Result
√72 = 8.4852813742
Simplified radical
Exact form
6√2
Decimal approximation
8.4852813742
Step-by-step explanation
- 1Identify the radicand as 72 and the root index as 2.
- 2Factor 72 as 36 × 2.
- 3Take 6 outside the square root to get 6√2.
- 4The decimal approximation is 8.4852813742.
How to Calculate a Square Root
2
Choose the root
Keep index 2 for a square root, or use 3 through 12 for an nth root.
3
Review each step
Check the exact form, decimal approximation, classification, and explanation.
Square Root Rules
Perfect squares
If n = a × a, then √n = a. For example, √144 = 12.
Simplified radicals
Factor out perfect squares: √72 = √(36 × 2) = 6√2.
Negative values
Even roots of negative values are not real. Odd roots remain real.
Nth roots
The nth root reverses raising a number to the nth power.
Square Root Calculator FAQ
What is a square root calculator?
A square root calculator finds the number that produces a radicand when multiplied by itself. It can also simplify exact radicals and show a decimal approximation.
How do you simplify a square root?
Factor the radicand into a perfect square and a remaining factor. For example, 72 equals 36 times 2, so the square root of 72 simplifies to 6 times the square root of 2.
What is a perfect square?
A perfect square is the product of an integer multiplied by itself. Examples include 1, 4, 9, 16, 25, 36, and 144.
Can you take the square root of a negative number?
A negative number has no real square root. Odd roots such as the cube root of negative 27 are real and equal negative 3.
What is an nth root?
The nth root of a number is a value that gives the original number when raised to the nth power. A square root uses index 2 and a cube root uses index 3.