How To: PHP - Roots in PHP (Square Root, Cube Root and nth Root)

To find the nth root of a number in PHP, we can use the pow(base, power) function, for example the cube root of 27 is equal to 27 raised to the power of 1/3, $\sqrt[3]{27} = 27^{1/3}$, since $3^3 = 27$.  In general the nth root of x, $\sqrt[n]{x} = x^{1/n}$.

To calculate the square root of a number, we can also use the sqrt(number) function.

Example

Some example code showing how to calculate roots in PHP is below:

<?php
// Square root
echo sqrt(49) . "<br />";  // square root of 49
echo pow(49,1/2) . "<br />"; // alternative to square root of 49
echo pow(8,1/2). "<br />"; // square root of 8

// cube root
echo pow(8,1/3). "<br />"; // cube root of 8
echo pow(27,1/3). "<br />"; // cube root of 27

// higher roots
echo pow(390625,1/4). "<br />";
echo "25^4 = " . pow(25,4) . "<br />";

echo pow(1234, 1/6). "<br />";
?>

The output from this example is as follows:

7
7
2.8284271247462
2
3
25
25^4 = 390625
3.2750594908837

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