What is the square root of 729?

1 Answer
May 23, 2018

Answer:

The positive square root is #27# and the negative one #-27#.

Explanation:

First find the prime factorisation of #729#:

#color(white)(000)729#
#color(white)(000)"/"color(white)(0)"\"#
#color(white)(00)3color(white)(00)243#
#color(white)(00000)"/"color(white)(0)"\"#
#color(white)(0000)3color(white)(000)81#
#color(white)(0000000)"/"color(white)(00)"\"#
#color(white)(000000)3color(white)(000)27#
#color(white)(000000000)"/"color(white)(00)"\"#
#color(white)(00000000)3color(white)(0000)9#
#color(white)(000000000000)"/"color(white)(0)"\"#
#color(white)(00000000000)3color(white)(000)3#

So:

#729 = 3^6#

Hence:

#sqrt(729) = sqrt(3^6) = 3^3 = 27#

This is the positive square root.

#729# also has a negative square root #-27#