开方计算器计算平方根、立方根和n次方根。
保存分享计算器如何使用 开方计算器1Enter the number2Choose square root, cube root, or enter a custom root3Click Calculate to see the result关于 开方计算器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.
开方计算器的主要功能Calculate square root (2nd root) of any non-negative numberCalculate cube root (3rd root) including negative number supportCalculate any nth root for a custom root valueDetects and confirms perfect squares with exact integer resultsShows the two nearest perfect squares for contextHigh precision output for irrational resultsInstant results without page reloadFully browser-based with no server dependency示例Square root of a perfect square
Compute the square root of 144 and confirm it is a perfect square.
输入
sqrt(144)输出
12 (exact integer, perfect square)Cube root of a negative number
Find the real cube root of -27.
输入
cbrt(-27)输出
-3 (exact integer)常见使用场景Evaluating radical expressions in algebra homeworkChecking whether a number is a perfect square for factoring exercisesComputing nth roots for exponential and logarithm courseworkFinding the side length of a square from its areaEngineering calculations involving radical expressionsQuick verification of square root approximations故障排除Taking the square root of a negative number in square root mode
解决方案
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
解决方案
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
解决方案
Perfect square detection only applies to positive integers. Decimal inputs will produce a decimal root without a perfect square classification.
常见问题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.