What is sqrt(187200) ?

2 Answers
Feb 3, 2017

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

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)