How To: PHP - Roots in PHP (Square Root, Cube Root and nth Root)
June 10, 2009 in PHP
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}](http://tiposaurus.co.uk/wp-content/plugins/latex/cache/tex_e4b15074e4e5cd63faf08437958927da.gif)
, since 
. In general the nth root of x, ![\sqrt[n]{x} = x^{1/n}](http://tiposaurus.co.uk/wp-content/plugins/latex/cache/tex_36016ebb1b1de6eb75941fc7286122a8.gif)
.
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
Midhun Girish said on July 22, 2009
Thanks for that man..it helped me really(i'm a little weak in maths...)
ikee said on July 26, 2010
great info.. thanks!
Aurelio De Rosa said on October 31, 2010
It doesn't work for negative numbers. For example pow(-8,1/3) = -2 but this method says NAN.
Tiposaurus said on February 19, 2011
Hmm, I must admit I never tried it with negative numbers. I think it might work for raising them to an integer power, but not otherwise.
I'm guessing it doesn't do that because there will be some situations where there are no real roots, e.g. sqrt(-1).
Meer Afghan said on November 14, 2011
Bundles of thanks it helps me in understanding the process
Produsa said on December 26, 2011
Thank u.