Square Root Calculator
Calculate square roots, cube roots, and nth roots.
How to Use Square Root Calculator
- 1Enter the number
- 2Choose square root, cube root, or enter a custom root
- 3Click Calculate to see the result
About Square Root Calculator
The Square Root Calculator computes square roots, cube roots, and any nth root of any number. Enter the number and the root to instantly get the result, displayed to high precision. The calculator also detects whether the input is a perfect square and identifies the nearest perfect squares above and below.
For the square root specifically, the tool shows whether the result is an integer (perfect square), an irrational number, or a complex number (for negative inputs). The nth root mode supports any positive root value, including fractional roots which are equivalent to exponent operations.
All computation runs in your browser with no server calls, making this ideal for students, teachers, and anyone who needs to quickly evaluate radical expressions without opening a full scientific calculator.
Key Features of Square Root Calculator
- Calculate square root (2nd root) of any non-negative number
- Calculate cube root (3rd root) including negative number support
- Calculate any nth root for a custom root value
- Detects and confirms perfect squares with exact integer results
- Shows the two nearest perfect squares for context
- High precision output for irrational results
- Instant results without page reload
- Fully browser-based with no server dependency
Examples
Square root of a perfect square
Compute the square root of 144 and confirm it is a perfect square.
Input
sqrt(144)
Output
12 (exact integer, perfect square)
Cube root of a negative number
Find the real cube root of -27.
Input
cbrt(-27)
Output
-3 (exact integer)
Common Use Cases
- Evaluating radical expressions in algebra homework
- Checking whether a number is a perfect square for factoring exercises
- Computing nth roots for exponential and logarithm coursework
- Finding the side length of a square from its area
- Engineering calculations involving radical expressions
- Quick verification of square root approximations
Troubleshooting
Taking the square root of a negative number in square root mode
Solution
Square roots of negative numbers are complex (imaginary). The calculator shows a note when the input is negative. Use cube root or odd-root modes for negative inputs, where real results exist.
Confusing nth root with exponentiation
Solution
The nth root of x is equivalent to x^(1/n). For example, the 4th root of 81 = 81^(1/4) = 3. Use the Power Calculator if you prefer to express it as an exponent.
Expecting a perfect square check for non-integer inputs
Solution
Perfect square detection only applies to positive integers. Decimal inputs will produce a decimal root without a perfect square classification.
Frequently Asked Questions
Can I calculate cube roots?
Yes. The cube root mode computes the real cube root of any number, including negatives. You can also set a custom nth root — for example, setting n=4 computes the fourth root.
What is a perfect square?
A perfect square is a positive integer whose square root is also a whole integer. For example, 1, 4, 9, 16, 25, and 36 are perfect squares because their square roots are 1, 2, 3, 4, 5, and 6.
Can I take the square root of a negative number?
Not in the real number system. The square root of -1 is the imaginary unit i. The calculator will note this if you enter a negative number in square root mode.
What is an nth root?
The nth root of a number x is the value r such that r^n = x. For n=2, this is the square root. For n=3, the cube root. For any positive integer or fraction n, the result is valid.
Is the nth root the same as a fractional exponent?
Yes. The nth root of x equals x^(1/n). For example, the square root of 25 = 25^(0.5) = 5. Use the Power Calculator to compute fractional exponents directly.
What are the nearest perfect squares used for?
Showing the nearest perfect squares helps you quickly estimate whether a number is close to a perfect square and what its approximate square root is.
Can I calculate roots of very large numbers?
Yes. JavaScript's number precision supports numbers up to approximately 1.8 x 10^308. For most practical purposes, any number you enter will be handled accurately.
Is my data private?
Yes. All calculations run entirely in your browser. No values are transmitted to any server.