170 BRAHMAGUPTA AND ARITHMETIC continue the process till all ghana-padas (cube-places) are exhausted). This will give the (cube) root (of the given number).¹ K.S. Shukla in his translation and commentary of this book has given the illustration of extracting cube - root as follows: Example To find the cube root of 277167808, Let us indicate ghana-padas or 'cube' places by "c" and aghana-padas or non-cube places as "n": n n c n n c n n c 277 167 808 Subract the greatest possible cube (i.e. 6³ or 216) from the last 'cube' place (i.e. from 277) and place the cube- root (i.e. 6) underneath the third place to the right of the last 'cube place; thus we have n n c n n c n n c 61167808 6 (remainder) (line of cube-root) Dividing out by thrice the square of the cube-root (i.e. by 3.6 or 108) the remainder up to one place less than that occupied by the cube-root (i.e. 611) and setting down the quotient in the line of the cube-root (to the right of the cube-root), we have n n c n n c n n c 7167808 65 (remainder) (line of cube-root) Let now quotient 5 be called the first' (adima) and the cube-root 6 the 'last' (antya). Then subtracting the square of the 'first' (adima) as multiplied by thrice the 'last' (antya) (i.e. 3x6x52 or 450) from one place less than that occupied by the quotient (i.e. from 716), we get 1. धनपदमयननदे द्वे धन (पद) तोऽपास्य धनमदो मूलम् । संयोग्य तृतीयपदस्याधस्तदनष्टवण ॥ २६ ॥ एकस्थानोनतया शेषं त्रिगुणेन (सं) मजेत्तस्मात् | लब्धं निवेश्य पङ क्त्यां तवर्ग त्रिगुणमन्यतम् ॥ ३० || जद यादुपरिमराशेः प्राग्वद् घनमादिमस्य (च) स्वपदात् । भ्रूवस्तृतीय पदरयाध इत्यादिक विधिमूलम् ||३१|| -Sridhara, Patiganita, 29-31
