What is sqrt(187200)187200 ?

2 Answers
Feb 3, 2017

432.666153432.666153

Explanation:

The square root of a non-negative number nn is the non-negative number which, when squared, gives nn 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

sqrt(187200) = 120sqrt(13)187200=12013

Explanation:

To simplify sqrt(187200)187200, first find the prime factorisation of 187200187200...

color(white)(0)1872000187200
color(white)(00)"/"color(white)(00)"\"00/00\
color(white)(0)2color(white)(000)936000200093600
color(white)(00000)"/"color(white)(00)"\"00000/00\
color(white)(0000)2color(white)(000)468000000200046800
color(white)(00000000)"/"color(white)(00)"\"00000000/00\
color(white)(0000000)2color(white)(000)234000000000200023400
color(white)(00000000000)"/"color(white)(00)"\"00000000000/00\
color(white)(0000000000)2color(white)(000)117000000000000200011700
color(white)(00000000000000)"/"color(white)(00)"\"00000000000000/00\
color(white)(0000000000000)2color(white)(000)5850000000000000020005850
color(white)(00000000000000000)"/"color(white)(00)"\"00000000000000000/00\
color(white)(0000000000000000)2color(white)(000)2925000000000000000020002925
color(white)(00000000000000000000)"/"color(white)(00)"\"00000000000000000000/00\
color(white)(0000000000000000000)3color(white)(000)97500000000000000000003000975
color(white)(00000000000000000000000)"/"color(white)(0)"\"00000000000000000000000/0\
color(white)(0000000000000000000000)3color(white)(00)3250000000000000000000000300325
color(white)(0000000000000000000000000)"/"color(white)(0)"\"0000000000000000000000000/0\
color(white)(000000000000000000000000)5color(white)(00)6500000000000000000000000050065
color(white)(00000000000000000000000000)"/"color(white)(00)"\"00000000000000000000000000/00\
color(white)(0000000000000000000000000)5color(white)(000)130000000000000000000000000500013

That is:

187200 = 2^6*3^2*5^2*13187200=26325213

So:

sqrt(187200) = 2^3*3*5 sqrt(13) = 120sqrt(13)187200=233513=12013