Question

What is `sqrt(187200)` ?

Answer 1

`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.

Answer 2

`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)`