What this calculator does
This tool tabulates and plots a root function over a range of x values. You pick the function — the square root, the cube root, or a general nth root — choose where the x range starts and ends, and set the spacing between points. It then computes y = the nth root of x at each sample point and presents the results as a table of (x, y) pairs and a line graph. It is pure mathematics and applies identically everywhere; no units or country rules are involved. Only real-valued results are supported (complex numbers are not).
How to use it
Select the Function. For the nth-root option, enter the integer order n (for example 5 for the fifth root); n is ignored for the square and cube root presets, which fix n at 2 and 3. Set "Range x (start)", "Range x (end)" and "Increment". The increment must be greater than zero and n must be nonzero. The calculator generates points x = start, start + step, start + 2·step, … up to and including the end value, capped at 301 points.
The formula explained
Each sample point is \(x_i = x_{\min} + i\,\Delta x\), and \(y_i = x_i^{1/n}\). For \(x \ge 0\) this is computed directly. For \(x < 0\) the real nth root exists only when n is an odd integer, in which case \(y = -\,|x|^{1/n}\); for an even root (including the square root) or a non-integer order, a negative x has no real result and is marked undefined.
Worked example
Cube root (n = 3), x from −8 to 8 with increment 4 gives x = −8, −4, 0, 4, 8. The y values are −2, −1.5874, 0, 1.5874 and 2. Because the cube root order is odd, negative inputs return real negative roots.
$$y_i = \sqrt[3]{x_i} = x_i^{1/3}$$
FAQ
Why is the square root of a negative number blank? Even roots of negatives are not real numbers; this tool does not handle complex results.
Why did my table stop early? Output is capped at 301 points. Reduce your range or increase the increment to cover the whole interval.
Can I use a non-integer order? Yes for non-negative x; for negative x a non-integer order has no real value and is shown as undefined.
