What is #sqrt(187200)# ?

2 Answers
Feb 3, 2017

Answer:

#432.666153#

Explanation:

The square root of a non-negative number #n# is the non-negative number which, when squared, gives #n# as the result.

There isn't really too much to do here. Trying to find a perfect square would be in vain, since the result is a decimal (with six decimal digits, mind you), so your best bet is to just use a calculator.

Feb 3, 2017

Answer:

#sqrt(187200) = 120sqrt(13)#

Explanation:

To simplify #sqrt(187200)#, first find the prime factorisation of #187200#...

#color(white)(0)187200#
#color(white)(00)"/"color(white)(00)"\"#
#color(white)(0)2color(white)(000)93600#
#color(white)(00000)"/"color(white)(00)"\"#
#color(white)(0000)2color(white)(000)46800#
#color(white)(00000000)"/"color(white)(00)"\"#
#color(white)(0000000)2color(white)(000)23400#
#color(white)(00000000000)"/"color(white)(00)"\"#
#color(white)(0000000000)2color(white)(000)11700#
#color(white)(00000000000000)"/"color(white)(00)"\"#
#color(white)(0000000000000)2color(white)(000)5850#
#color(white)(00000000000000000)"/"color(white)(00)"\"#
#color(white)(0000000000000000)2color(white)(000)2925#
#color(white)(00000000000000000000)"/"color(white)(00)"\"#
#color(white)(0000000000000000000)3color(white)(000)975#
#color(white)(00000000000000000000000)"/"color(white)(0)"\"#
#color(white)(0000000000000000000000)3color(white)(00)325#
#color(white)(0000000000000000000000000)"/"color(white)(0)"\"#
#color(white)(000000000000000000000000)5color(white)(00)65#
#color(white)(00000000000000000000000000)"/"color(white)(00)"\"#
#color(white)(0000000000000000000000000)5color(white)(000)13#

That is:

#187200 = 2^6*3^2*5^2*13#

So:

#sqrt(187200) = 2^3*3*5 sqrt(13) = 120sqrt(13)#